Can you have a car loan in your name and someone else carry the insurance on the car in the state of New Jersey?

You cannot insure a vehicle that you do not own. I have had to say this about fifty times in answering questions and it does not change. If you do not have an insurable interest (own or co-own) the vehicle then you cannot insure it. The policy must be in the name of the person who owns the vehicle and all household members and other possible drivers must be listed as drivers on the policy. The only exception to the owner being the insured is when the two are husband and wife. For instance if the policy is in the husbands name and the care is in the wife's name that is alright. I always list the named insured on the policy as both spouses so that either one can make changes on the policy, add or delete vehicles, sign any documents needed, etc.