Puff appears 67 times at rank 1564 on male pets. The name has two simultaneous cultural references pulling at it — the nursery rhyme dragon and Sean Combs's longtime stage name — and owners using it are rarely thinking about both at once. Most are responding to the texture or appearance of the animal in front of them.
Descriptive Naming Logic
Puff as a pet name is primarily physical: the dog or cat has puffy, fluffy, or cloud-like fur, and the name is a direct observation. This puts it in the same category as Fluffy and Cloud — names that function as affectionate physical descriptions. The simplicity is the point. Pomeranians, Bichon Frises, and chow chows are natural recipients.
The Pop Culture Layer
Puff the Magic Dragon from the 1963 Peter, Paul and Mary song remains a genuine cultural anchor for the name. Puff Daddy adds a second layer of association for owners who came of age in the 1990s hip-hop era. Neither reference is particularly heavy, which makes the name feel light and playful rather than weighted.
The Counter-Reading
Puff works best on visually appropriate dogs and loses some of its charm on short-coated breeds where the physical logic doesn't apply. On a greyhound, the name creates a pleasant absurdist gap. On a Bichon, it's simply accurate. Both can work, depending on the owner's sensibility.