In Idolm@ster 2 I named my unit Nemurihime, which was named after the Nemurihime manga. The unit in that manga was also called Nemurihime and consisted of leader Chihaya, Miki, and Haruka (which was the same unit I used). Nemurihime is also the name of a song that Chihaya sings.
I decided to call my unit in One for All Nemurihime to keep it consistent. Of course, I later realized that in One for All you produce all idols, so calling it Nemurihime didn't make much sense. But, you can't change the name once you've decided. Oh well... At least, my best idols in that game are Chihaya, Miki, and Haruka.