Rabbit
If I have an Animal named "Random", which animal would it be? A Rabbit. Raccoon, Rat, Raven, Reindeer, or a Rhino?
A rat or rabbit
I think a raccoon would fit.
A Rhino seems kind of random . . . It's the only one that seems to be from its own region of the world.
Roadkill
I think I would give that name to my pet reindeer. "Random Reindeer" - yep, I like the sound of that. :)