When I was in third grade, we picked up a stray cat my aunt had found. My 4 y/o sister was terrified my dad wouldn't let us keep the cat, so she named her Bun Bar, after my dad's favorite candy bar. (She only ever answered to Bunny, though.)
Gotta love that child logic.
The year before, when we got my cat, she named him, too: Captain Kangaroo. Again, we only ever actually called him Captain.
My current three were inherited from my parents, so they all have Hawaiian names: Ka'anapali (Pali), Israel Kamakawiwoʻole (Izzy), and Mia (I have no idea what that one is short for - most likely another beach).