Me me me!
I change Frog to Glenn, but I also change Magus to Janus. That's it.
Crono is Crono because, well, that's who he is.[/li][/list]
Marle remains Marle because she is incognito and is using a travelling name, so she obviously wouldn't use her real name. However, I would change her name after the reveal of who she is if the game allowed. I always use my head canon to just assume that Marle is actually her middle name and a nickname of sorts, even before meeting Crono, so that's why she sticks with it even after revealing that she's Princess Nadia.
Lucca remains Lucca because she's Lucca.
Ayla also remains Ayla. I never saw a reason to change it.
Robo remains Robo because his serial number, R-66Y, is just so impersonal. The whole point in Marle changing his name was to give some pizzazz and some personalization. Prometheus doesn't fit, but it's also just an assumed name given to him from Mother Brain during the whole robot rebellion. Once he forgets it all and chooses to help Crono and company, he technically is no longer Prometheus; that part of his memory is corrupted and gone, so it doesn't make sense for him to go by Prometheus. I should note in my first two or three playthroughs I did change his name to
Iron, but now I stick with Robo.
Frog, as I said, remains Glenn. He lost his human form and honor, but he is still Glenn. I'd like to think when he finally claims the Masamune and regains his sense of self, he does so as Glenn, not as a false identify of Frog.
Magus, to me, is dead by the time the party gets him to join the team. I don't mean a literal death, of course, but rather mean that, well, Janus is reborn. As Beach Bum stated, Janus was no more after the Ocean Palace disaster. He shed his identity and became Magus, manipulating the Mystics/Fiends and pushing the boundaries of his body in order to enact his revenge against Lavos. However, after coming full circle, confronting the loss of Schala (again, quite literally reliving the event), he sort of sheds the life he lived as Magus. He no longer acts or considers himself the Fiendlord, and he steels his resolve to continue to defeat Lavos and save Schala. To me, I always felt like Magus regains his sense of self and comes to terms with who he really is (as Janus) after those events, and thus I name him as Janus to recognize that, to me at least, he regains his sense of self lost so long ago.