Oddly, in The Big O, there was a cat named Perro.note Though, in Japanese, "pero" is also the onomatopoeia used for cats licking themselves (Japanese has no double-R), giving an alternate explanation for the name.
A partial example of this is found in One Piece, where there are at least 2 Fishmen that are named after the fish they're based on. Their names are Jinbe and Daruma. The former is a whale shark Fishman (In Japan, whale sharks are called "jinbee-zame") and the latter is a cookie cutter shark Fishman (cookie cutter sharks are called "daruma-zame" in Japan).
This is omnipresent in Pokémon. While the species names are either Pokémon Speak or Verbal Tic Name, it's a little weird that nearly every pet Pokémon is named after its species.
In Pokémon Special, trainers who bother nicknaming their Pokémon usually give nicknames that barely deviate from the species' name anyways. In fact, White is the only nicknaming Dex Holder who gives her Pokémon regular names, albeit slightly punny ones. In an interesting variation, X gives his Pokemon nicknames based off of their French names.
The heroine of Princess Tutu is a duck who can turn into a human girl. Her name is Duck. Often she's still referred to by her Japanese name, Ahiru... which is Japanese for "Duck."
Ranma ˝: Subverted by Kodachi's pet, Mister Turtle, a crocodile.