After Kira tells Sonny she is one of the Greek muses, she starts to say, "My real name is Terp" but Sonny shushes her and she never reveals her real name. She is there to help him open a dance club, and she is obviously a dancer, so her name is most likely Terpsichore, after the Greek muse of dance--although in the stage adaption of the film she was Clio, muse of history.
The soundtrack was an enormous success. The song "Magic" went to #1 on the US pop singles chart. In the UK the soundtrack album peaked at #2, and the single "Xanadu" was #1 for two weeks in July 1980.
According to the special features on a recently released DVD, the cartoon sequence was added because the filmmakers needed to include an extra song written for the movie. Having a cartoon made for the song was easier than trying to make it fit into the movie.