Jr in the pet registry is almost certainly an abbreviation — not a deliberate two-letter name, but a shorthand for Junior. This is a paperwork artifact: owners who call their dog Junior sometimes write Jr on licensing forms, treating it as the official registered form. The intent is a name rather than an initial, but the distinction collapses in a municipal database.
Registry Artifact Context
Municipal licensing forms don't enforce name completeness. An owner who writes "Jr" likely calls the dog Junior day-to-day — a name with its own warm tradition of being given to dogs who share some quality (size, manner, or literal family relation) with a person named Junior. The data entry is the anomaly; the name behind it is conventional enough.
The Junior Tradition
Junior as a pet name has a long, affectionate history. It implies a dog who came second — after an older dog, after a family member, after something. The "Jr" shorthand carries the same implication. It suits male dogs with a slightly deferential personality or, conversely, dogs named in ironic tribute to someone much larger. Chihuahuas named Junior have a specific ironic charm.
The Counter-Reading: Register the Full Name
If your dog's name is Junior, registering him as Junior rather than Jr keeps the record clean and avoids the dog being officially named a legal abbreviation. Junior is the intended name, and it's a warm, perfectly good one. The two-letter version is a form-filling shortcut, not a naming choice.