In the 1980s, I read a story in an anthology, and I think it was relatively new at the time I read it. I would like to locate it again, but I don't recall anything else about the author or what kind of anthology it appeared in.
The main character was immortal (or more likely he was just very long-lived; he himself did not know for sure). He had been born in Roman times, but his growth and development had stalled when he was about fifteen, leaving him looking like a teenager for millennia. (I think the story made the point that it was very annoying to him that he had spent so long not being taken seriously as an adult, by folks much, much younger than him. However, I could be confusing this element with Leigh Brackett's "The Jewel of Bas.")
Finally, in the present day, he has reached maturity and is now looking for a mate. He has been dating three or four different women, while wearing different disguises. However, it turns out that they are also all the same person, also using disguises and also immortal. The pair are initially ecstatic, until he finds out that she is only 400 years old, and they will have to wait another thousand years before she will be sexually mature and able to reproduce.