Papa appears 67 times at rank 1562 on male pets. This is almost certainly a registry artifact in the majority of cases: a family affectionate term that ended up on the official paperwork when someone submitted the microchip or license application using the nickname they actually called the dog around the house.
The Paperwork Artifact Problem
Pet registries capture whatever owners write down, and owners don't always write the formal name. Papa functions as a term of endearment in many households. It appears alongside similar artifacts like Daddy and Buddy in the registry data. The actual count of dogs genuinely named Papa as a chosen name is likely a fraction of these 67 records.
When Papa Is a Real Choice
Some owners do name dogs Papa intentionally, often large, calm breeds who take on an elder-statesman quality within a multi-dog household. Great Danes and Saint Bernards fit this aesthetic well. The name also connects to Hemingway's famous nickname, giving it a literary register for owners who want that layer.
The Counter-Reading
Papa as a deliberate name requires a dog big enough in personality to carry it without irony. Small dogs named Papa create a comedic mismatch that either lands or doesn't. On the human side, the given name parallel is essentially nonexistent. This is pet territory.