I have known several people who had Yorkie pups that the hair just didn't grow as fast as some of the other Yorkie pups that other people had. A good friend of mine has 5 Yorkies and one of hers had short hair like that until she was several months old and she is lovely now (she is several years old).
It looks like a Yorkie to me and like babies who some have long hair by the time they are a few months old and some are nearly bald until they are toddlers. It is all genetics and I would not judge it by how long their hair is.
Sit back, relax and I hope that you enjoy your puppy. Most likely than not it is a purebred Yorkie if you bought it as such. I would not worry about it too much.
Enjoy and welcome to Yorkie Talk.
__________________  It's raining Yorkies here! LOL Teek  ,Rowan  , Raksha (Grand Puppy)  , Raelyn  |