Usagi

Associated with the moon as in Japanese tradition a rabbit is seen in the shadows on the moon, not the man as in European tradition.

Actually, it isn't too uncommon to see a girl named Usagi in Japan. It's just that the Kanji used to spell it doesn't mean "rabbit". I've seen it spelt so that it means "heron's feather/wing", "full moon", and several other ways that I can't recall at the moment.