If we are talking about the person in the Battle Tower lobby, than mine was a Lass, I believe, but I have not gotten to battle her yet. I probably haven't talked to her enough yet.
It depends on your Trainer I.D, and your gender.My freind used a Gameshark to cheat (I still didn't forgive him) to change his name, and he got a different person, for the battle frontier, and his secret base.