My cat's name is Rowan, but he only gets called that when he's in trouble. Most of the time I call him Tub because he's, well, large.

Back when Rowan was his only name, he used to flip out when I had baseball on and the Cardinals happened to be playing the Phillies; every time one of the broadcasters mentioned Scott Rolen, the cat would stare at the TV, trying to figure out why they kept saying his name.
My parents' Lab is named Molly, but she also goes by Wally, and their Shih Tzu's name is Max, but I think I'm the only one who ever calls him anything else (Maximilian).
The funniest was my brother's yellow Lab, Sable. That was the only thing we called her until one morning when she was a puppy and heard us talking about bagels and thought we were talking to her, so then she was Bagel. That devolved into Beagle, which in turn became Beeg, then Beegie, then Beanie, then Beanie Weenie, and finally Beans, which is what we ended up calling her most of the time.
Oh, and sometimes we call Molly "Mittens" because of a cute Christmas ornament I saw in some catalog that had a dog on it and was personalized with that name. Don't ask how we transferred the name to Molly; my family's just strange that way.