Bunny \b(un)-ny\ as a girl's name is of English origin. Nickname deriving from B- names such as Barbara or Bernice. Now used as a child's name for a rabbit. Likely to be associated with the famous Playboy Bunnies. Bunny has 3 variant forms: Bunnee, Bunni and Bunnie. For more information, see also the related name Bonnie. Baby names that sound like Bunny are Bonny, Binny and Benny. View a list of the 3 names that reference Bunny.