
Although KC registration is taken on trust, fact is without registration papers, you have no guarantee you have anything other than a Yorkie-type puppy I'm afraid. I hope you didn't pay KC Reg. Yorkie prices. The puppy is cute of course but you have to hope she lives a long and happy life with you, with minimal need of a vet!
If somebody regularly registers puppies with the KC and falsifies the information, pretty soon they will be caught out btw. If only by fellow-breeders. Could be that the parents weren't KC registered however, meaning although they just might be purebred, any offspring couldn't be KC registered.
For next time, even if you don't want to show or breed, buying a puppy from a reputable breeder who does register what they produce, should mean all the puppies in the litter, show or pet, should benefit from being well reared, from breeders who do their homework before putting Dog A to Bitch B.