How did you do that?
According to this brief summary of state requirements a non-resident is NOT ALLOWED to register a motor chicle in New Hampshire or South Dakota.
drivinglaws.aaa.com
I didn't review the entire list but I don't think any state allows a non-resident to register and title a motor vehicle.
I know it's possible for a person could probably falsely claim residence by using someone else's address but it would not be legal.
Some retirees who are full-time rv travelers use a mail service in SD but even though they don't have a permanent home addresss they claim residence and vote in SD.