Can your son insure your car with a different company with same definitions?

In most U.S. states anyone can insure a car for liability purposes, But it is unlawful to insure the property of another or property in which one does not have an insurable interest.

So, if your son wants to buy full coverage on your car, he would have to list the owner on the policy as well for it to be a legal binding insurance contract. Otherwise, if the vehicle was damaged and the insurance company discovers that your son is not the legal owner, they would be required by law to deny payment for the sustained damages since he is not the owner.