In rough lists from most significant relationships to least. Quick note: it doesn't matter how often you tell him your name, he will never use it unless you've got his full attention. Nicknames are based on whether you do something memorable while he's around. Most of the people he likes have them. All Exorcists get them.
blackwhitedeparted
Road
Allen Walker (cheating boy)
Cyril
Nagi Naoe
Nanako
Hikaru Shidou (burning girl)
Miranda Lotto (clock girl)
Namine (cleaning girl)
Setsuna
Florian (wishing boy)
Rain
Luck Gandor (boss)
Misao Makimachi (betting girl)
Rinoa Heartilly (garden girl)
Seifer (boasting boy)
Lady
Sam Oliver
Andy Gallagher - black - salting boy
Aziraphale - black - magician
Belial - white - boss
Howard Link - black - inspector
Lenalee Lee - black - Road's Doll
Obito Uchiha - white - ninja boy
Zolf Kimblee - white - boss
[name]: Tyki Mikk
[age]: 26 + 1 City year = 27
[status]: employed at the Cassagioso by one Zolf Kimblee. Since then, it has changed hands to one Luck Gandor.
[for action threads]: It varies between white and black. Black is nearly always wearing really nice clothing and/or smoking. His skin goes to a sort of meatish-grey color and his eyes turn gold, so he can't really be mistaken for hobo mode. White always has horribly ugly coke bottle glasses on, and he will let you try them on if you ask nicely. He's got a tan and sometimes he smells a little, but not much.
[abilities]: To sum it up, Tyki can choose what he wants and doesn't want to touch. This enables him to do all sorts of neat tricks, like walk on water and air, and... reach in and pull out someone's internal organs without touching anything else.
He can also summon man-eating golem in the shape of butterflies, which he keeps in himself when they're not in use. They can be converted into energy blasts and shields, although he doesn't seem to rely on this much.
Lastly, he can switch between two forms - which he calls the White and the Black - both of which are well within the boundaries of what counts as human. He maintains the same powers in both forms, but he's more likely to avoid using anything supernatural while playing White. Theoretically, there's a third form where a bunch of tentacles burst from his back and he bleeds black, gets an all-around stats boost, and becomes virtually unbeatable, but that shouldn't come up.
[character history / background]: Little is known about Tyki Mikk's life before he appears in the manga. From the flashbacks of other Noah and his own state, however, we can assume that he grew up an orphan, and that he led a normal life before the Pleasure of Noah got him. Whether his current hobo lifestyle was his former life or whether it was a side-effect of becoming a Noah - in order to enjoy a normal human life as well as life with the Pleasure - hasn't been revealed yet. We can also assume that becoming a Noah happened a while ago, since it takes a while to adjust to the state and he exhibits a distinct comfort with the family that seems unlikely if the bond were new.
Since then, however, he's been living a double life in two forms - white and black. White lives the ordinary life of a hobo, traveling from town to town with a small band of friends, cheating at poker, working at mines and whatever else it takes to survive. Black lives under the Earl's orders, killing Exorcists, breeding Tease and having a fun time all around. He switches comfortably back and forth between the two, and seems to have achieved a stable balance between them by separating them completely.
This continues until he meets Allen Walker through a chance game of poker while in white form. In which he was scamming Allen's friend (Crowley / Krory / however the cool kids spell it) out of all his worldly possessions, of course, but that's not the point. The boy, in turn, cheats him mercilessly out of house, home, and pants.* At the end of the game, Allen gives back the possessions he won from the band. In return, Tyki tosses him a pack of cards to remember by. All seems well.
Until the Earl of Millennium calls Tyki for a job: to erase everyone connected to Cross Marian -- Allen's mentor.
Falling into his black form, Tyki obeys him with pleasure. He kills a few Exorcists and change, and drives another insane before sending him back to the Exorcists singing about the Heart. This state of affairs drags on until Allen Walker shows up again. This time, the fight's not a metaphor - and Tyki loves it. Standard shonen battle ensues - with an unlikely result. Tyki unleashes a few of his abilities before destroying Allen Walker's Innocence** and opening a hole in his heart. Then, last name crossed off the list of those to kill, he scatters the cards he gave Allen over the boy's (presumably dying) body and takes off to entertain himself until the Earl calls him again.
* This would be true if he had a house. Or a home. Sentiment still applies.
** Which is the name of the weapon he fights with and not the bad metaphor you're thinking of. Stop that.
[character personality]: At first, it seems as if Tyki should be fairly simple to understand. Since he holds and represents Noah's Pleasure, he's governed first and foremost by the pleasure principle. If it should please him to do a thing, he does it - regardless of the consequences. In this way, he lives two lives. As his white self, his pleasures are simple and human; as his black self, his pleasure is to kill. His existence balances on the edge of both.
“We're a wandering band of light-fingered orphans~”
On the white side, Tyki is your ordinary hobo: good-humored, slightly dishonest, willing to eat anything so long as he can have his fill. He's acquired quite a number of vices over time: smoking, drinking, (cheating at) gambling, et al. In theory, with his mind and manners and powers, he could achieve a good job and be moderately well-off, but that wouldn't be any fun. Good jobs mean putting down roots, and attachments are not for the Tyki-hobo. Besides, odd jobs are always more interesting, and tell him so much about people.
Although he can put on refined airs, he doesn't bother unless there's an occasion to be met. This isn't to say that he doesn't have a certain degree of pride. He's not fond of being insulted or condescended to, and won't put up with it unless the person in question matters to him. That's not an easy bar to reach. Possibly as a product of so much frequent wandering - or because of it - he doesn't get attached easily, though he's friendly enough. (After all, it's hard to cheat someone if they don't trust you first.) He does have a fondness for like minds - people who aren't vicious, but true to their natures and live their lives for the fun of it all - and a bit of an interest in people who show no fear. (Really no fear, not that haphazard overcompensation some heroes do in the face of danger.)
For all that he's had no education, he can think on his feet and is quick to react to any precarious situation. Years spent living on the winnings of poker and whatever he plucked out of a passing purse have taught him how to spot a mark in the crowd. Despite this, his judgment misfires on occasion, usually to his own spectacular loss. For the most part, he's a decent appraiser of people, though he doesn't bother unless they do something that strikes his interest.
“What I love, I destroy. I love humans.”
In his black form, Tyki's hardly recognizable. He loses the uneducated accent and picks up a certain grace and bearing peculiar to the upper class. Some constants remain. He takes care to enjoy things just as he did before. He's as lazy about the duller pursuits as ever: he won't find a job or cook, to the point where he will eat raw fish from a lake. (While it's still wriggling! He pulls out the bones first, of course.) As well, he still likes people who share his perspective and lies by omission and roundabout wordplay instead of direct untruths. The only difference are the pleasures. Instead of amusing himself with poker and alcohol, his black form turns to murder.
For Tyki, there's fun to be had in the fight as well as the kill. He loves a challenge, savoring the thrill with an intensity that blocks out all else. Obviously, he tends to go after exorcists most often, since they're the only ones who offer any sort of difficulty given his powers. He takes his time over death scenes, throwing in little twists and complications. A time or two, he's even driven someone mad and left them singing thin, crazed songs. It's never about killing someone as much as it is about utterly breaking him or her. The point is in the artistry.
Outside of killing, he tends to drift. He doesn't stay long unless there's a job to complete, since killing bystanders presents no challenge - unless an exorcist is watching, of course, but that's a different matter. Presumably he appreciates the same things as he does in his white form, but he tends to avoid this so as to minimize the common factors between white and black. In a way, though, he's just as easy to befriend in black as he is in white: you have only to catch his interest.
The fact that the only people he really interests himself in are a) Noah b) Exorcists c) powerful in some other way d) all of the above is beside the point, of course.
Tyki's loyalties lie with himself, first and foremost, and then with the Noah and the Earl of Millennium. Everyone else falls outside the circle. Though he might be fond of one or two, his feelings don't change the fact that they're expendable. If necessary, he'd kill them and delight in every minute of their murders. It's not in his nature to regret for long and Tyki would never deny himself something he'd enjoy. In fact, this is the reason he uses for going along with the Earl's plans - because he enjoys the havoc. Noah, however, fall outside of that category; he sees them not only as kindred creatures, but as family. People he would kill for - though this doesn't mean much.
“The white side and the black side... Having both of them is what makes it so enjoyable!”
The fact that these two lives lie at such odds with each other means that in order to maintain both, Tyki has to keep them strictly separate. People from his white life don't know the details of his black life; people from the black side don't enter or interfere with the white side. This doesn't stop him from using the same name in both forms, however. The explanation for that's simple. No matter how hard that makes it for him to keep both white and black in a closed environment like the City, both forms are Tyki Mikk. To give one a different name implies that it's a disguise - something less than the other - or that he changes somehow in the transformation and becomes someone else. He doesn't.
Tyki loves to live. Tyki loves to kill. And he lives as he must in order to wring out the best from both. Easy as that.
*