The 3 year and 1 year vaccine is the exactly the same, the only difference is the label. This was done by the manufacturer because some states required the vaccine to be administered at one year intervals and some allowed the three year vaccine. To get around this the manufacturer just changed the label.
You don't have to go to the same vet to establish some sort of record with him. As long as you have the pups records you can go to any vet.
These links are quite helpful explaining the rabies vaccine....
What to Do Before Your Dog's Rabies Vaccination | Truth4Dogs How to Vaccinate Against Rabies More Safely | Truth4Dogs