If My Cars Insurance Is In My Name But The Loan Is Under A Different Name Can It Be Reported Stolen?

The person that holds the loan is the owner. The owner can report it stolen. But, if when police arrive the driver can show proof of insurance, registration and payment agreement, in most cases they will allow that person to keep possession of the car, then inform the "owner" that he/she must file in civil or claims court. States vary, check with your state dmv. Or better yet try calling you presiding local law enforcement. This is of course between adults of legal age, who have both entered into a written binding agreement.