You can name your characters in all for the first four games.
In FFI, you pick their names at the beginning.
In FFII, you choose the names of the four main characters, but the other characters (i.e. Minwu, Josef) have predetermined and unchanging names.
Once again, in FFIII you choose your characters' names at the beginning of the game.
In FFIV, names can be changed by Namingway in almost every city of the game.