I don't know all the lyrics by heart, but growing up, I've heard this song over and over again. Then, I thought it was some chick being sassy and just randomly saying "that's not my name" as a sad way of "sassing off". I dunno. Kid thoughts, right?

But now, I would say that, like the others have said, she's tired of people not knowing her name. I'm afraid even after this hit song people still don't know her name even many years later. Maybe she's tired of being called "that one chick in that one band" instead of her actual name.