Jill appears 66 times at rank 1575 on female pets. This is a generational human name landing in the pet registry: the dog-naming equivalent of the demographic wave where owners name pets after the human names they grew up with rather than choosing something pet-specific.
The Generational Human Name
Jill was a top-200 baby name in the United States from the 1950s through the 1980s, peaking in the 1960s. Owners giving that name to a dog now are almost certainly in the generation that grew up alongside Jills, treating the name as warmly familiar rather than dated. It sits alongside Janet and Linda as a mid-century female name that reappears in pet registries. The human name comparison is at /names/jill.
Sound Fit
Jill is one syllable, direct, and impossible to mispronounce. For a pet name, that's functionally excellent. Short names carry across a park, don't get mangled at the vet, and feel natural in rapid repeated use. The name fits any dog or cat the owner has decided to treat as a person, which is a growing category.
The Counter-Reading
Jill on a dog reads as charming or mildly odd depending on the audience. People who know Jills will smile; people who don't may find it unremarkably generic. Neither reaction is wrong. The name's plainness is its defining quality. There's nothing to explain or defend.