I never had a game where you could change the name until I started watching my stepdad playing FF2 (4j, whatever you want to call it) on SNES. Man, he was cool. Lol, he renamed all the characters after our family.
The funniest was when he renamed Kain the Dragoon to "Spud" which was my stepbrother's nickname (because his head was shaped and looked like a potato).
Anyway, I always use the defaults, because it's too difficult to match up real names with guides or conversations with other players. The only time I name characters on my own is when there isn't a default name, and I always name the guy Leon, because I think that name is bad ass.