Well, technically speaking, the last game you could name everybody in was III..the NES version anyway. After that, you could name the first party member for a while...and then afterward, they started just giving them all static names.

That's kinda why I want to play one of the updated versions of the original game and why I'm considering emulating the NES version of III. xD So I can go through it with the names of friends or characters. xP