Mozzarella, after Joey made him depressed.
Mozzarella is the name Joey gave to a dog that Phoebe borrowed to help him cheer up after he becomes upset over his obsession with Rachel, in "The One With The Birthing Video".
Phoebe calls him the happiest dog alive. Joey felt a little comforted and enjoyed playing fetch with him, but after he pours his heart out to Mozzarella, the dog becomes miserable and Phoebe takes him home.
The dog belongs to Phoebe's friend Wendy. It is unknown what breed he is.
At one point, Joey says, "You're a guy, right?" before checking Mozzarella's legs and finding that the dog was castrated (neutered), to which he says, "Well, you used to be".