To start off with, do you have a severe mental or physical condition that prevents you from functioning in your normal day to day life? If the answer is no, then he should not be a service dog no matter how badly you would like him to be.
If the answer is yes, there is a lot you have to research. As scarfish said, the likelihood that your puppy just happens to have the drive, temperament, and nerve to handle service work is very low. If you are lucky and he does have it, then you will likely have to buckle down and do a lot of owner training. You can get help from a professional experienced in training service dogs (who usually go by word of mouth, I've never heard of a trainer from a non profit teaching outside of their company) but you will basically be putting in the equivalent of a small part time job working on his training every single week. Do you honestly have time to log 8-10 hours a week? To extend a ten minute grocery trip for milk into an hour long socialization/working session?
People typically get service dogs as older, already trained dogs from a company that raises and trains them because many dogs do wash out of service work simply because they cannot genetically handle it. Even when it's deemed they can handle it, they have to have the working drive necessary to maintain handler focus and carry out service behaviors even in challenging situations. For example, my dog alerts to oncoming panic attacks. It doesn't matter if we are sitting in my bedroom or some strange lady in Walmart is grabbing his collar and cooing over him, he has to ignore pretty much everything else and reliably alert to my panic attack. That takes a lot of training and it's not something you can do only half way.
I would also suggest going to ADA.org and educating yourself on the laws surrounding service dogs. There is no official certification, test, or training program for a dog to become a service dog. To have a service dog, the handler must have a debilitating mental or physical condition and the dog must provide an active service (his service can't just be that he makes you feel better, he has to perform a behavior) that prevents, mitigates, or helps reduce the handler's disability. Also, while not specifically in the law, it is generally expected among the service dog community that a SD blends in with the public. It is not there to stand out. Therefore a service dog is completely housebroken, does not bark, growl, whine, or solicit attention from people, never sniffs or damages product when in a public environment, maintains a walking pace with the handler without lagging or forging, and is able to ignore all of the various abuses the public often doles out on a service dog.
There is no one company that is "approved" or "official" in any legal way when it comes to service dogs. There are quite a few that train them, but they go through appropriate training and are matched with disabled handlers that need them. But this does not make them the only people who can train service dogs, nor does it make their service dogs any more or less legitimate than owner-trained or independently trained service dogs.
I feel like there is still more I might be missing out on, but I know there are others here as well that are also service dog handlers.
In short, any online service dog registry you find is a scam and if you think there is a legitimate one, you need to do a lot more research.