Short answer: No
Can you insure a vehicle that is not registered to you, and the answer is no. The car registered solely in your name will only have validated insurance to declare a claim if that car is owned by you.
Whatever the case is, trying to obtain insurance on a vehicle that you may use regularly but the car is not registered in your name It’s best that the registered owner’s Insurance policy has your name on it also. However, the policy may be null and void if a claim is made and it proves the insurer is not the owner of the registered car.
So make sure that your insurance policy follows how your vehicle is registered with the DMV.
If there’s a cosigner, you want to make sure that both names are on that insurance policy. Frequently it’s common that parents that are helping out their son or daughter. But never a good idea when it’s a boyfriend/girlfriend situation.
Don’t get caught in a situation where an accident has occurred where you’re at fault, or a lawsuit is pending, and you don’t have coverage.