Corey shows up 58 times in the registries at rank 1737, skewing male. It's a classic middle-register American given name — neither distinctive nor anonymous — and as a pet name it operates firmly in the ironic-human-name tradition: giving your dog a name that sounds like it belongs to your neighbor's kid from 1987.
The Generic Human Name Effect
Corey is the quintessential Gen X name : popular in the 1980s through Corey Haim, Corey Feldman, and the general cultural momentum of that decade. As a pet name today, it belongs to owners who grew up with that name as ambient background noise and are now deploying it with full self-aware irony. It's the same register as Chad, Brad, or Kevin ; these are names where the joke is the cultural ordinariness itself.
Human-Pet Crossover
The human name Corey has declined significantly since its 1980s peak, which makes it available and unambiguous in the pet space ; there's very little risk of naming your dog after a current human Corey in the household. See the full human naming trajectory there.
Counter-Reading
Corey on a pet is a specific joke that lands best when the pet somehow embodies a particular 1980s-suburban-kid energy. If your dog actually does have that quality — earnest, slightly disheveled, endlessly enthusiastic — the name achieves a rare coherence between animal and label.