I usually don't change them since I know them by their real names already. If I'm playing through a second time I might change their names just for fun, but still refer to them as their actual names.
I always change "Dagger" back to "Garnet" in FFIX, because Dagger is a stupid name, and the first time I played FFX (the first final fantasy game I played) I named Tidus "Sexy!" I also renamed the aeons, but I don't remember all their names...
Playing through FFX again, I named everyone after different elements of pizza.
Tidus was "Pizza" and the aeons were named things like "Crust," "Sauce," "Cheese," "Mushroom," "Olives," and all that sort of stuff.
I also played FFVII again and renamed many of the characters after my dogs, myself, and my sisters. But I named Tifa "Tits." Don't go crazy on me though... I don't hate Tifa. I just hate it when the main female character in anything has to have huge tits and a tiny outfit... They know what they did too... That's why her outfit is so much less slutty in Advent Children and in other FFVII related media.