You need to call your old insurance company.

You don't have to call the rmv, just update it next time u renew your registration. but if the car is under loan with a bank, you should Definitly call the bank and let them know you have switched insurance, because the old company can send them a letter saying undropped coverage and the bank will repo the car.

It won't be a problem if u get pulled over, just keep your new policy in the glove box.