A Great Dane and Chihuahua mix is not a popularly recognized breed; it is either a hybrid or a mixed breed. Hybrids or designer dogs are created by mating dogs of two different pure breeds. A dog of unknown ancestry with Great Dane and Chihuahua traits is a mixed breed.
Designer dogs are bred to incorporate the most desirable traits of the parent breeds. Puppies born to the original can vary widely in size and appearance, and breeders attempting to create a consistent type continue selecting for desired traits as they cross the hybrids with one another or with one of the parent breeds. Mixed breeds have a more random genetic background than designer dogs, and only DNA testing can confirm if a mixed breed shares common ancestry with a given pure breed.