Yes, they do. Yes, puppies do shed the fur that they are born with. It makes way for an adult coat as and when they progress towards maturity. The shedding happens around four to five months, but it also depends upon which breed we are looking at.  Sometimes, the shedding is so much that the pup is left with nothing but patches of hair on its skin. Do not worry, for slowly but surely, your dog will start growing a smooth and steady coat, which will last for a lifetime.