I'll just stick to the current pets, there have been too many others to list.
Bailey, the dog, came with her name. She was 4 and knew it well, and we still keep in good contact with the family who gave her to us. I can't think of a better name for her, though I do sometimes shorten it to Bea.
Morgan, a cat, has her name because I love that name and DH won't let me use it for a kid.
Murphy, the other cat, because that was the name I thought of when I met him, and it suits him.
Jose (Cuervo) is the fish. He is named Jose, because when we got him we had Bailey (Irish Cream) and (Captain) Morgan.
Charlie is the horse. And his name is twofold. First, his real name is Entwistle Wy Bar, and that's a mouthful, so he was called Sorrelly when we got him. Which is descriptive of his coloring, but I got tired of explaining it to people who don't know the real name of horse coloring. Charlie was the closest easy name to Sorrelly. Plus, now he's my Charlie Horse.