Haha, I have never named my fish, except once when I was little and I got my first angelfish. I called the striped one Kramer because he moved erratically and the gold one Elaine (both after Seinfield....I don't know why lol).
Otherwise, whenever I talk to my fish I call them by their common names, like "Mr. Parrotfish" (for my blood parrot) or "Mrs. Zebra Danio". Very creative huh?
My aunt calls my blood parrot "Tang" because he is bright orange.
I have known cats named Cat Kitten and Kitty. They were barn cats though so they were more like staff than pets.
I think naming cats makes more sense than naming fish though. The only name I have for anything aquatic is Quasimodo, my somewhat deformed ACF.
My cat's name is "Mr. Kitty".