Wow. There are fake musician LEGO minifigs! They don't so much have names as occupations, but what can you do. Pop Star is from Series 2, set 8684 LEGO Minifigures. She comes with her own microphone!
In the short-lived online computer game LEGO Universe, this character appeared with the name Gwen Tweenbangle.
From her online bio at LEGO.com:
The Pop Star is at the top of the charts. Her last three albums went platinum and her videos are in non-stop rotation on all the music channels.