The age and name of Athos
Athos states that he is 48 at the start of 'Twenty Years After' (Ch 14), which would have made him about 28 at the end of 'The Three Musketeers. I think (although I'm not sure), that The Three Musketeers takes place over about 2 years, so Athos would have been about 26 at the beginning of the story.
However, in Athos' story about his 'friend' who hanged his wife, he says his 'friend' was 25 when he fell in love with Milady, who was 16 at the time, which doesn't really give him enough time to find out Milady was branded, hang her, desert his position, join the Musketeers and become inseparable with Aramis and Porthos.
Aramis is 22 or 23 at the start of The Three Musketeers (Ch 2). In Aramis' retelling of his own history (Ch 26), he was 3 days from 20 when he was threatened by a gentleman for reading 'Lives of the Saints' to the ladies; for a year he trained daily with the best fencing master in Paris, and on the anniversary of his being insulted (i.e. when he was effectively 21), he challenged the gentleman to a duel and killed him. He likely met Athos and Porthos during that year of training:
'Athos, whose acquaintance I made about that period, and Porthos, who had in addition to my lessons taught me some effective tricks of fence, prevailed upon me to solicit the uniform of a Musketeer. The king entertained great regard for my father, who had fallen at the siege of Arras, and the uniform was granted.'
So how long had Aramis been a Musketeer before the start of the book? About two years at most. He would have known Athos for slightly longer than that - which suggests there was at least two and a half years between Athos meeting Anne (Milady) and becoming a Musketeer, which there isn't time for if he was 48 'Twenty Years After' after the book.
Perhaps 'Twenty Years After' was a generalisation and it really means 'Roughly Twenty Years After'?
In fact, there's a timeline here that puts the events of The Three Musketeers as occurring between 1625-1628; Twenty Years After occurred during 1648-1649.
But if Athos states that he's 48 in 1648, he would have been born in or around 1600, and he would have been 25 at the beginning of The Three Musketeers, which isn't compatible with the story he tells of when his 'friend' first met Anne (Milady).
Perhaps we can discount the age that Athos gives for his 'friend' as him trying to anonymise the story. But he does outright state that he's 48 at the start of 'Twenty Years After'. Which still does make him 25 at the start of The Three Musketeers.
In 'Twenty Years Later', there is this exchange between d'Artagnan and Porthos:
"And then he [Athos] was older than any of us," added D'Artagnan.
"Some years only. His gravity made him look older than he was."
So if Aramis and Porthos are around 22 or 23, and Athos is around 25 at the start of The Three Musketeers, that could work. He just seems older because he was well educated, depressed and an alcoholic. (In fact, Bonacieux estimates Athos to be 'thirty at least' in the Three Musketeers(Ch 13), while estimating d'Artagnan to be 'scarcely nineteen or twenty'. Fun fact: Constance was also 23! (Ch 17, T3M))
One last calculation is that Athos is 62 at the end of 'Ten Years After' (Ch 56), which the timeline says happened in 1661; again, that puts his birth being around 1599 or 1600.
And if Athos knew Aramis when the latter was 20, I'm guessing he would have joined the Musketeers at the latest two years before the book and perhaps at least three, making him at least 23 (or perhaps even 22) when he joined the musketeers. At a guess then, he was between 21 and 23 when he met, married and hanged Milady, and not 25 as he described his 'friend'.
If Milady's age was correctly given in his story (although as discussed, I don't think his 'friend's' age was correctly given), she was 16 when she met Athos and she would have been around 20 or 21 at the start of T3M. That's pure speculation though.
The conclusion to all that? I think Athos was likely 25 or 26 during the Three Musketeers; but either Dumas was not great with timelines or Athos was not being factual when he said he was 25 when he met Milady.
I can't find any reference of Athos' given name throughout the books; Wikipedia says that the character was inspired by/got his name from the historical musketeer Armand de Sillègue d'Athos d'Autevielle (although that's all he seems to shared); it also says that the character of Athos was named as Olivier in Dumas' play 'The Youth of the Musketeers'. (Interestingly, Wikipedia says that Milady/Anne was named Charlotte in the play, and while Athos knew her as Anne de Breuil, she later used the name of Charlotte Backson when she met Lord de Winter.)
I always imagined that 'Athos' was a completely assumed name and one which had no ties at all to his given name or family titles. Athos is a mountain in Greece where women are forbidden, and I had always thought that our Athos was romantic and dramatic enough to take that as a name and signifier for himself.