Dotty is a female pet name with two readings: a diminutive of Dorothy (meaning "gift of God"), or a British colloquial word for slightly eccentric. Both work well on a pet, and the best owners appreciate both at once. It's warm, vintage, and has an immediacy that invented names lack.
The British Eccentric Register
Dotty as a personality descriptor, "she's a bit dotty," is British English that has filtered into American usage with enough charm. It fits pets with erratic, endearing behavior. Dalmatians, with their literal dots, are an obvious match that doubles as a visual pun.
Vintage Name Aesthetic
Dorothy and its nicknames (Dot, Dotty) were common early 20th-century names that have become vintage-pet-name territory alongside Millie, Bessie, and Mabel. Basset Hounds and older-breed dogs suit these names particularly well. See the human comparison at Dorothy.
Counter-Reading: Eccentric Is a Commitment
Calling your dog dotty (eccentric) with the name Dotty is either very funny or slightly unkind depending on the dog's actual personality. Make sure the name fits the animal, not just the joke. Dottie with an IE is slightly more common and equally charming.