I was going to do this in chronological order, but I'd end up repeating myself a bit, so I'll start with traits he exhibits first and keep moving from there. This is a personality write-up. Oh, and it has spoilers. Who'd've thunk it, right?
I am very disorganised I will dump things where I want to. >:|
This was originally intended for me to sort out my thoughts on McDohl's personality as the games progressed, following the choices he would make necessary to get the best ending.
**This is really messy and rambling because I haven't edited it for readability or grammar.
So when Suikoden begins, you have Tyr with his father before their audience with the Emperor. From the way Teo speaks to Tyr, telling him to 'just be himself' followed by the later option to tell the Emperor 'I don't wanna', is one example of how, at the beginning, Tyr is rather ill-mannered. Further evidence of this comes in with the options to tease Gremio and Pahn, and Cleo telling Tyr that she's told him before to knock before entering a lady's room. In addition, if Tyr speaks to Marie at the end, she asks if he teased Gremio too much and doesn't want to go home now! His dialogue choices in the beginning also show his ill-mannered and childish side with things like 'I dunno' and 'Somewhere on this earth.'
He's also very impulsive and adventurous at this stage, with even dull errand missions being something of an adventure with his friends. Riding a dragon to Magician's Island, taking out mountain bandits who had been stealing tax money, these things seemed to ignite some sort of drive for adventure and heroism. Even after becoming the Commander of the Liberation Army, Tyr still has the option to jump right into things like taking down Kwanda Rosman who planned to destroy the Great Forest and kill all the elves with it in spite of the fact the Liberation Army isn't that strong yet.
Tyr's childish side fades away to virtual non-existent after Kwanda is defeated at Pannu Yakuta (at which time Mathiu declares that the battle has made Tyr a man). His dialogue choices become more formal, for instance. Yet he doesn't entirely lose his childish side. He can still tell Joshua, the Leader of the Dragon Knights, that the matter they want to discuss with him is that Tyr would like to fly on a dragon (rather than ask for their assistance). That choice is met with a 'Be more serious!' sort of line. He can also continue the joke between Ledon, Kessler, and Ronnie Bell when he meets them at the Secret Factory.
I haven't yet touched upon his daddy's boy side, which as I played the game, he was one to the end, though you do have the options to refuse and refuse to fight Teo, Tyr ultimately has to do it because he's more 'Leader of the Liberation Army' than 'Teo's boy' by that point... Teo treats him as such when he challenges Tyr.
Anyway, the very beginning of the game as Tyr following in Teo's footsteps by enlisting in the Imperial Army. The biggest thing holding Tyr back from joining the Liberation Army is his loyalty to the Empire. More than that, though, it's because of how devoted he is to his father, one of the Five Great Generals. For the early part of the game, one of the things Odessa says to try to persuade Tyr to join the Liberation Army is to ask if he plans to be 'McDohl's boy' forever, and this can be seen as their official parting of ways.
Also, in the city itself, Tyr is basically eclipsed by his father's popularity and image. A guard outside the McDohl household shouts at Tyr for wandering around by General Teo's house without even realising that Tyr is the son! In addition, when Tyr and the others try to escape through Kwaba Fortress, the commander and an old friend of Teo's, Ain Gide, convinces the guards that Tyr couldn't be Teo's son because his son obviously wouldn't dress like a beggar.
As the game goes on, the ties between Tyr and his father become almost entirely severed. Teo is even sent to the north at the beginning of the game in order to crush the rebels. At the time of the battle with him, Teo makes it clear that they are completely different and that he intends to kill his son, who has become the most wanted man in the land. In the end, however, when Teo is dying, his last words are to say that he's proud of Tyr and the man that he's become. He orders his two right-hand men to aide Tyr in his chosen path. According to Cleo, Teo had a look of content as he died. This coupled with the manner by which Teo died and the fact Tyr was crouching beside him as he did probably made Teo's death all the more painful to Tyr than if his father continued to renounce him, though I also think he becomes another one of those people whose dying wish he must fulfill by winning the war.
Thus far, it would have been hard to tell that the Tyr of Suikoden I is anything like the one seen in Suikoden II, but now I'll move further into Tyr's character development.
One of the major ways in which he develops is as a leader. Really, he was just a rather ordinary fourteen-year-old kid at the start, and it's only because of Viktor wanting him to meet Odessa that Tyr even becomes entangled in the Liberation Army and, really, she's one of those characters who, despite dying, are never really forgotten. Like Kircheis, but that'd be more if the story was told from Flik's point of view, which it totally isn't.
Wow I get off topic.
But anyway, Odessa really influenced his decision, initially, to join the cause of the Liberation Army. She points out that he can go back to his comfortable life in Gregminster, but he can't ignore what he sees around him. I think this is the seed that really influences the rest of his decisions and speaks a lot about his character in that he cannot simply turn the other cheek when he sees something unjust taking place. This is pretty much every decision to get involved ever. Yet when it gets to the second game, even though the desire to help still exists, he's stopped being so impulsive because of fear of the rune, which did react when Riou and his party told him about a child which had been kidnapped by bandits. Suikoden II stuff should really be held off for now, though.
But yeah, Odessa was held up through-out the war as a person that Tyr had to measure up to. Admittedly, it's to be expected when they cover up and he's only the 'acting leader' in the beginning so that the small Liberation Army wouldn't cease to exist without her. According to Mathiu, Odessa had intended for Tyr to be the next leader (which she did hint at to Tyr directly before Kage interrupted them in one scene). No-one lets Tyr ever forget this.
Nevertheless, Tyr slowly proves himself to be a reliable leader. In my opinion, this is mostly thanks to Mathiu and his guidance, especially in recruiting Lepant who proves to be a loyal and powerful general to the end. Although he doesn't openly admit it until near the end of the war, Mathiu was just as committed to winning the war at any costs, ultimately costing his own life, as Tyr had been.
There's a lot to be said on what Tyr was taught makes a good leader as well as what makes a good person, and it seemed like when those two conflicted, he was a leader in battle but a person afterwards. In order to get the best ending in the game, Tyr is not allowed to kill any of the Great Generals that he defeats (because they are Stars of Destiny). One can only speculate why, but I think it's related to the fact that Tyr believes it's wrong to kill them because they were being controlled by Windy and forced to commit those crimes. While he usually gives into the wishes of his men, he doesn't allow himself to be swayed by their hatred to not look objectively at the situation.
And really, that seems to be the most important thing for a leader as far as the Liberation Army has taught him. He has to keep fighting even though he might not want to anymore. Unlike Riou, Tyr is never given the option to run away from it forever. In addition, it seems that to be nice might not always be the best quality in a leader, according to Viktor who must love him some Machiavelli says that to Tyr regarding allowing Gremio to come along (continuing to protect him like a child) to Soniere Prison to save Liukan. The mission ultimately resulted in Gremio's death, which seemed to be the real end of Tyr's childhood. As we leaves his room, the things the others say to him become progressively less sympathetic and seemed more designed to let Tyr know he cannot show weakness and even though Gremio, who was a father-figure to him, just died, he must lead the subsequent attack on Scarletia himself. By the end, he must go on in order to not disappoint Odessa or waste the life Gremio gave up to save Tyr's. Yeah, that comes up quite a bit, too.
So yeah. Leaders have to keep going in spite of tragic events. As more people around him die, he seems to be able to pick himself up more easily and continue on to the point where when it comes to his best friend, Ted, dying, even though he's disturbed (with the same lack of music that's present in all the other death sequences), he's able to continue the mission to its end.
Responsibility is a large part of his character. It would be a lie to say he isn't responsible, and he seems to want to please people, but he sticks up for his ideals first and foremost. Both Gremio and Teo's last words echo this sentiment that he should always do what he feels is right. And really, it seems that obeying those last words are important to Tyr. He kept Odessa's death a secret because it was her wish, and when it's finally his time for him to relay the message of her death, he has trouble doing so. This is also why I think he spares all the generals, ignoring what others want. When Milich's head is on the chopping block, he has to say that he is not at fault rather than saying that Gremio must be avenged. (Milich was the one who killed Gremio, but like Kwanda, he was controlled by Windy when he did so.) That is basically as objective as you get. It's the same as for when he hesitated to help save the child at the beginning of his run in Suikoden II: Even though he would want to save him, he doesn't know if that would be a wise choice because the Soul Eater reacted.
Hm, regarding Ted, I really think I should write on him since basically everyone else got a little something of their influence. Ted was really Tyr's best friend, and his place in Tyr's heart is really shown by the fact a portrait of him hangs in his room in Gregminster. I don't think Tyr was mad at Ted for killing himself as he did, but rather, it all really influenced how he viewed the Soul Eater. But this is about Ted. Since Ted doesn't get much of an appearance in game, I really think Ted was mostly if not entirely purely Tyr's greatest friend. The player sorta has to assume this, but with all of Ted's words to Tyr, it's pretty obvious how much they care for each other. Since it's Ted that Tyr speaks about to Kasumi in the Gaiden, I think that Ted can't ever really be forgotten by Tyr.
When it comes to the Soul Eater, though, and everything he's told about it, it's no wonder that Tyr believes it's evil (according to a comment made by Gremio in Suikoden II). What Ted said before he died, about how the rune is evil, taking the souls of Odessa, Gremio, and Teo to gain power, probably sealed this belief, but Windy stating that she believes herself to be the ideal host for the rune doesn't help the 'this rune is evil' image. Leknaat warns Tyr to never use his rune, and more likely than not, he follows through.
In the Gaiden, which takes place after Suikoden II, Tyr seems to be coming more to terms with the rune and his view seems to shift from that of 'the rune is evil' to something that... I guess is easier for him to accept. Since it contains the souls of those that he loves who came together and defend him against Windy in the final battle, I think it might be that he accepts that while its intentions are evil, it also contains the souls of those who are not.
Tyr probably would keep the rune forever and ever regardless of his feelings towards it, though. He saw what Ted went through as a child and the responsibility he had to bare from that point until about three hundred years later when he gave the rune to Tyr. He took a break sometime during those three hundred years, but Tyr doesn't know that. The point is that Ted and his grandfather both gave their lives to protect the rune, so now that responsibility passes on to Tyr.
I want to mention the scene where Lepant attempts to give Tyr the throne after they go to the Toran Republic for the child they rescued to see Liukan (apparently Tyr's idea from Gremio's dialogue). While Lepant is hard on him, still treating him and seeing him as Commander Tyr, Tyr still refuses by just backing away from the throne. I think that, probably, Tyr was avoiding the need to be a leader any longer after Suikoden I and his escaping into the night. He passed the seat onto Lepant because he saw Lepant as someone who could be a competent leader, which he was. Eileen's dialogue suggests that she sees Tyr more as a boy than as a leader now, and one that needs to be out and exploring as young boys like her son do. Lepant probably makes him promise to return for the throne some day, but as he's still not there after fifteen years, one has to wonder if Tyr ever wants to take the position. Or maybe he's waiting for Lepant to die. Who knows.
Other things in Suikoden II, even though I probably skipped a lot of important character things in Suikoden I still, is that I sort of see that there is some development in his character from the boy who ran away for three years after the war was over to one who slowly tries to return to that old life. When they return to Gregminster, Gremio reveals that the reason Tyr hadn't wanted to return home was because of the painful memories surrounding it. Given that the last time he lived in that house with Gremio, Pahn, and Cleo, Ted and his father were still alive, it's not that hard to see why Tyr might not want to be there for a while.
But he does stay there, and he joins Riou's team when Riou goes and fetches him (although Gremio tells him to be back by sundown). This at least shows that he isn't completely against being with other people, both familiar and unfamiliar (as there are Suikoden I recruits that are also Suikoden II recruits). And in Gaiden, after the events of Suikoden II have ended, Kasumi is seen visiting Tyr while he fishes and he opens up to her about his thoughts and is able to speak a bit more normally, like he had before. He takes her to lunch, even! Since Kasumi's ending changes to her visiting Gregminster weekly if Riou meets Tyr, it can be assumed that she probably visits Tyr once a week following the war. I think it's nice, and take it as a sign that he probably is slowly building relationships again. So he's not stuck as always being the morose person shown in the main events of Suikoden II, basically.
On the traits he does exhibit in Suikoden II, he seems very serious, and often times has nothing to say or only spares a few words. What he does say is usually practical and honest, but he seems to work, in regards to Riou, from the perspective of a more hardened leader to a new one. When Riou tries to run away, he has no words for him before he walks away, and if in the throne room Riou wants to wait for Jowy as the building comes down, Tyr tells him his life is too important. In my view, he likely rehashes what he learned as a leader himself and passes it onto Riou. I don't think this would still be the case others, though. It's probably just because Riou is a leader with the hopes and dreams of many resting upon him, like he had, that Tyr treats him that way.
One thing I don't get with fanon is having Tyr always be the sort to smile falsely? When in Suikoden I, there are mentions of his expressions, and usually it's to say he doesn't look happy but rather usually looks morose (by Viktor), and Windy points out how he looks angry. Given how he seems like a pretty honest guy in general, I don't think he would smile falsely. He probably put up a false front before the troops, but I don't think he'd have a reason to pretend otherwise.