The first cat that my kiddo got was a rescue and was given a new name. The cat didn't seem to mind and DID come when called the new name.
Maybe dogs are different...I don't know.
I suppose a new name would be OK once the dog (or cat) realizes it belongs to him or her.
I like the idea of Opera Names.
“Mephistopheles” has a nice ring to it, for a cat. :-)