They would be Chihuahua x Yorkshire Terrier crosses. Or are you asking about the generation designation? If both parents are Chi x Yorkie crosses, then they are considered F1, and their puppies would be considered F2. Once you get past the first four of five generations of crosses, then they are just considered mixed breeds.
Mutts, like the parents.
I'm not sure why people think mutts with "breed names" aren't still mutts. Mutts are great, should not be intentionally bred though unless every shelter and rescue group is out of business because every dog has a home.