Pony is a species-adjacent name — you're calling a dog or cat after a different, smaller equine — and that cross-species naming choice is always a deliberate irony or a sincere affection for the word itself. At rank 3150, Pony appears 27 times in the registry: each instance is almost certainly a dog whose gait, size, or energy reminded the owner of a small horse.
The Cross-Species Irony
Naming a dog after another animal is a classic comedic move in pet naming — see also: Bear, Moose, Bunny, Fox. Pony sits in this tradition, and it works best on dogs with a distinctive movement pattern: Standard Poodles with their prancing gait or large dogs who trot with natural elevation. The name is a visual observation and a small joke simultaneously.
Childhood Desire Fulfillment
Every child who asked for a pony and got a dog instead has a parent with exactly this energy. Pony as a pet name for a dog is the kindest possible resolution to that original disappointment — the owner has decided to collapse the categories. This is a name with a very specific emotional backstory.
The Counter-Reading: Confusion Potential
Calling a dog at the park by yelling "Pony" will generate stares. Owners need to be comfortable with that mild social disruption as a standing condition. Browse playful names at pet names.