I'll make some general observations that might apply if your dog is pure-bred. The long-haired dogs you see at dog shows always look impeccably groomed, with long, flowing fur. That is because they are brushed every day, often multiple times per day. Long fur tends to tangle easily and/or break as a dog runs around, rolls around, or simply lies down, and if the tangles are not removed promptly they begin to form mats. Dogs with fur that touches the ground may have that fur tied up and protected when the dog goes outside. In other words, keeping that coat in show-quality condition is a very time consuming and arduous commitment. It also means that the dogs may not be able to run and play freely.
This is why you will rarely see dogs with long perfect coats in everyday life. Many people have their dogs clipped periodically because shorter hair is much easier to brush and keep tangle free. Matted fur is painful for the dog, and must be removed. It is likely that the dog on the right was clipped (received a haircut).
I have a Bearded Collie that I keep in full coat (I never have her fur shortened by clipping). But she does not look nearly as good as a Beardie in a dog show. I do thoroughly brush her twice a week, but that is not enough to keep her coat completely mat free. When I cut mats out, the coat loses that overall smooth look. And the day after I brush, the fur get tousled and begins to tangle, so that perfectly groomed, flowing look is gone.
So to answer your question, if your puppy is a pure-bred Yorkie, it is possible to have him look like the dog in the middle if you are willing to put in the time and effort. You can also have them groomed, leaving the coat longer than the dog on the right as a compromise: He will be easier to keep in good coat condition and look more like the dog in the middle than the one on the right.