Most Japanese people would not name a child "Usagi". In fact, some might even laugh (maybe quietly to themselves) if they heard that a couple had inflicted that on their daughter. [noted -ed]
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.
-- Anonymous User 9/4/2006
In the manga Tsuki no Shippo (Tail of the Moon) by Tinko Ueda, the main character is named Usagi.
-- Anonymous User 8/15/2008
This name is soooo cute. I'm naming a character this. ^-^