Judge appears 63 times at rank 1627 on male pets. It's a title-as-name, the kind of choice owners make when they want to give their dog maximum authority before the dog has done anything to earn it. The name is a bet on personality, or a joke about the dog's tendency to give disapproving stares at everything.
The Authority-Name Register
Judge belongs with Duke, Baron, and Captain: titles that confer status rather than describe it. The difference is that Judge implies evaluation. A dog named Judge is always being watched, and the name frames the dog as the one doing the watching. This lands particularly well on breeds known for serious, assessing expressions: Bloodhounds, Chow Chows, any dog that looks like it has opinions.
Sound and Calling Distance
JUHJ is one syllable, authoritative, and stops cleanly. It projects well. The lack of nickname options means owners who choose Judge are committing to it fully. You can't affectionately shorten it into something gentler. The human name is at /names/judge.
The Counter-Reading
Judge works best on a dog with the bearing to carry it. A stoic large breed named Judge grows into it every year. A golden retriever named Judge will spend its life undermining the brief with excessive friendliness. The name is a wager, and it either pays off or becomes a running joke.