Is it normal? My 2-year old suddenly wants to change her name!?

2 years is sometimes the age they want to start getting freedom. It's the age they begin their self confidence and want to do things by themselves. It could just be her trying to figure out who she is and wanting a little freedom from what YOU decided her name would be. At 3 my daughter insisted her name was Jade. It was just a phase like an imaginary friend.