Professor is an occupation title used as a pet name. Like Chef, Judge, or Major, it works through the gap between the dignity of the title and the reality of the animal. A dog named Professor carries an implied joke about intellectual authority that the dog will immediately undermine by eating something off the floor.
The Title-as-Name Tradition
Giving pets professional titles is a long-standing comedic naming tradition. Professor implies both academia and a certain prim, bespectacled authority that translates to either a cat who looks perpetually skeptical or a dog who sits with unusual stillness and appears to be judging. Both readings are intentional by owners who choose this name.
Pop Culture References
Professor appears as a pet name in multiple television contexts: Professor Wigglesworth, Professor Biscuit, and similar combinations appear across social media as owners lean into the title with an appropriate second name. The character of "the Professor" from Gilligan's Island (resourceful, slightly pompous, ultimately charming) is also a plausible reference for owners of a certain generation.
The Counter-Reading: Requires the Right Dog
Professor needs a dog that performs the role at least a little. A dog who stares thoughtfully, tilts his head during conversation, or sits with unusual dignity makes the name land. A chaotic, hyperactive dog named Professor creates a different kind of comedy: equally valid, but more ironic than affectionate.