There is NO official way to register a dog, so don't let any websites convince you there are. There are a ton of sites out there who cell "certificates", ID badges, vests, patches etc that designate service dog - but just know that you don't need ANY of that stuff legally...only if you want that stuff (like, a vest is sometimes good). Even Amazon sells patches and vests.
Legally, service dogs are allowed everywhere, whereas ESD dogs aren't quite as ubiquitously allowed. You can be asked what your dog does / is trained to do - but they CANNOT, by law, ask you about your disability -- it is against the law to do so.
I'm attaching a little card I made for my mother in law....
__________________ ~ A friend told me I was delusional. I nearly fell off my unicorn. ~ °¨¨¨°ºOº°¨¨¨° Ann | Pfeiffer | Marcel Verdel Purcell | Wylie | Artie °¨¨¨°ºOº°¨¨¨° |