It The Divorce Papers Request This. Most Likely His Name Is First On The Note. After The Divorce It`s His, If You Let Him Have The Vehicle ( Which Is Fair ).Don`t Worry I`m Sure It Won`t Affect Your Credit & If Not Paid For, It Will Be On Him. Best To You If you can get access to the truck, put it in storage somewhere and offer to let him have it back after he gets your name off the loan. You may want to talk to your attorney about that first though, just to make sure it's legal.