Can you request a check for damages from the insurance company of the driver who caused the accident and not get your car repaired after an auto accident?

It depends on if you have a lien placed on your vehicle (by you lender. If you own the car free and clear, you can take the insurance money and not repair the car, but if there is a lien on your vehicle more often than not the insurance company will make the check out to you and your bank.