I have a cat named Muddy. (because when they were all tiger kittens, his stripes were the least distinctive, so I kept referring him to the one that's kind of "muddy colored".) Funny how names stick.
I have a mouse named "Mouse Puppy". That started as a joke when my at-the-time boyfriend rescued her and gave her to me, and she was still a baby. He said "Look, it's a mouse puppy!"
I have a Silkie named Rachel, which I think is rather dramatic for a chicken, but I let the carpenter's son name her, and that's what he chose. A deal's a deal.
Then I have two other chickens named Gray and Blackie. Totally unoriginal, but creative names just never stuck for them.
Oh, and now I have a stray cat that comes up on my porch at night and I've been feeding him. I've been calling him Porch Kitty.
A lot of other pets too, but those are the oddest names I suppose.