There's two different possibilities as I see it in regards retaining mind and identity.
If you become the mind of a rabbit... well you're not really you any more; you're just another rabbit.
1. You become an animal, or whatever, and fully retain your memories and reasoning processes. Basically, mentally, everything stays the same except the form your mind possesses. You're the same "you", you're just in the body of an animal. The old Justice League Cartoon had an episode with this premise where Diana/Wonderwoman was transformed by Circe into a Pig.
2. You're transformed into said animal/whatever and you're just a witness to its behaviors. Essentially your meat transforms into animal/demon/whatever and you become a passive witness in your own body forced to only be able to watch but have no agency. Essentially you have a first person point of view of the life story of some other being. Note that if your character/morality/mental identity change you're not really "you" any more. "You" as we consider a sense of identity/action, no longer exist in such a scenario.