Some gender-neutral C names for dogs are Claymore, Coby, Codi, Coleen, Conner, Crews, Cruz, Crystal, Danica, Davey, and Darcie. Claymore is an unusual name that can be used for either male or female dogs. Coby is a unique name that can be used for any breed of dog, while Codi is perfect for a sassy pup. Coleen is a classic name that can be used for both male and female dogs, while Conner is perfect for a spirited pup. Crews is an all-American name that can be used for any breed of dog, and Cruz is perfect for a pup with energy and character. Finally, Crystal is elegant and classy, Danica is beautiful and unique, Davey is cute and cuddly, Darcie is pretty and feminine.