Both of your names must be on the policy. Otherwise, one of you could be left without coverage if you divorce or separate. Especially important for young drivers whose rates can often be much higher than other drivers. Make sure your teen is insured to drive only the least expensive car you own, not all of the cars you own. Consult your insurance company.
States have differing laws and rules concerning claim filing.
Make sure to check with your State Insurance Commissioner prior to withholding a claim to your provider. Your insurer will charge you the higher rate until you furnish appropriate proof. You back out of your driveway and scratch the side of your car on your mailbox. Always file a claim if the damage involves another driver. You may be tempted to pay for a fender-bender yourself and not report it to your insurance company.