Pup is almost certainly a registry artifact. At rank 2668 in the NYC and Seattle pet licensing data, "Pup" is the word owners and shelter workers write on forms when the dog doesn't have a name yet, when the owner is still deciding, or when the formal name was left blank. Some entries may be intentional (owners who genuinely call their dog Pup), but the majority of the 34 records almost certainly represent incomplete paperwork rather than a naming choice.
The Placeholder Artifact
Pet licensing databases at this tier accumulate words that were written on forms without functioning as actual names: Pup, Dog, Pet, Puppy, Unknown. These appear consistently across city datasets and inflate the apparent diversity of pet names. The honest reading of Pup at rank 2668 is that most of these dogs have real names. Their owners simply didn't write them on the license form. Compare Dog and Puppy for the same pattern.
The Intentional Use Case
That said, some owners do call their dogs Pup as a deliberate name: usually rural or working-dog contexts where the animal's function is foregrounded over naming convention, or households where the puppy grew up being called Pup and the nickname became permanent. Border Collies on working farms occasionally carry names this functional.
The Counter-Reading: It Doesn't Name the Dog
Pup describes what the animal is, not who it is. As a name it offers nothing distinguishing: no story, no identity hook, no sound that belongs uniquely to this specific animal. Owners who want to honor the simplicity without the blankness might consider Kit or Bub instead.