If a deer hit your car and you have full coverage who does the insurance agency send the check to?

You submit the claim to your insurance company and they should send the check to you minus your deductible. If there is a lien on the car, the check will go to either the shop that does the repairs. If the repairs are not made the check may be made to the lender AND the owner or only to the lender. The named insured on the policy and the loss payee if there is one.