Rosy appears 59 times in the registries at rank 1728, strongly female. It's an adjective name — rosy-cheeked, rose-colored, optimistic — that functions as a complete character description embedded in a single word. Naming a pet Rosy is making a claim about their personality before you've finished the paperwork.
The Adjective-as-Name Tradition
English adjective names for female pets have a long history: Sunny, Rosy, Merry, Jolly. They describe a disposition rather than an appearance, and they set an expectation that the pet will meet. Rosy in particular implies warmth, pink-tinged health, and a generally optimistic temperament. It suits social, affectionate breeds where those qualities are observable. Sunny and Daisy are its closest neighbors in this register.
The Color Connection
Owners with pink-nosed or light-coated pets — white dogs, pale cats — sometimes use Rosy for the color reference as much as the personality one. There's a visual coherence to a white Bichon Frise named Rosy that's hard to argue with. Browse Bichon Frise names for the full soft-and-white category.
Counter-Reading
Rosy, as a name, sets a specific temperamental expectation that not every pet will meet. A shy, anxious, or territorial dog named Rosy creates mild irony; charming or tiresome depending on how often you have to explain it. The name also skews quite young and sweet, which may not fit a larger or more imposing breed.