I remember when I sold our Saturn car directly to a private party, I logged onto the state DOL (department of Licensing) web-site where I could inform the state of the sale of my car.
All my other cars were trade-in’s for new cars, and never had a problem. I did not bother informing the state. The dealer must have taken care of ownership transfer.
I traded in a Pontiac one time. I continued to receive license renewal notices for the next two years. I ignored them. I guess the dealer never resold that mini van.