The robot in Lost in Space answers to "Robot", even among those who consider it family and best friend.
The Emergency Medical Hologram in Star Trek: Voyager never found a better name than "Doctor". That's not just Everybody Calls Him Barkeep: being a Doctor is more than what the EMH does, it's what he is (though he eventually learns to transcend his programming).
"Horse" from Monkey. "Horse" is really a dragon named Yu Lung, but everyone just calls him "Horse".
Somehow comically averted in Gossip Girl, since Chuck's dog gets named Monkey".
The Lass family in Dead Like Me adopts J.D. without knowing the meaning of his initials. Reggie decides it's "Just Dog".
Played with in one episode of Wizards of Waverly Place. They get a dog named Dragon, but it's actually a dragon magically disguised as a dog.
In the premiere episode of the final season of 24, Jack Bauer asks his granddaughter if she's given a name to the stuffed bear he got her at the zoo - she says that he's "Bear."
JAG: The dog Admiral Chegwidden adopts in the season nine episode "Empty Quiver" is named Dammit, because that was the only expression to which it would pay attention.
He's eventually re-named to Riot, but the Australian Shepherd Sam hits with the Impala in Season 8 of Supernatural is initially just called Dog.
Power Rangers S.P.D. has Kat Manx, Fowler Birdie, and Sergeant Silverback, who are both aliens that resemble anthropomorphic animals that match their names. Anubis Cruger, who looks like a dog, is also called by the nickname "Doggie" (in Tokusou Sentai Dekaranger, he actually was named Doggie Kruger.) Piggy, however, is a subversion; he doesn't really look like a pig.