I pulled out my old copy of CC today, because I'm the kind of person who replays games they've already beaten multiple times in their hours of leisure rather than be productive. I discovered something interesting though; you can't rename Serge "Crono" at the start of the game. You can name him quite literally anything but Crono. The game simply refuses to accept it as a name and forces you to enter something else.
I encourage anyone with a copy of the game to try it out for themselves, because I had never even heard of it until now. It's interesting there's still things we're learning about a game released roughly 12 years ago.