pub quiz

Charles Dickens used the pen name Boz but I dont know that he had a dog called that

Dickens's dog was, I think, called Turk. And you're quite right, it was Dickens himself who wrote under the pseudonym "Boz".

A quick Internet search shows that Senator James Phelan (first popularly elected Governor of California) had a beloved pet dog called Boz. But no doubt others did too.

On the assumption that this is an English pub quiz, I'm not sure that Phelan is the best answer...

Giler.