If a child drives his parents car which is insured under the parent's name will he be covered?

You will have to add him to your insurance. He will be under your name and your premium will go up! if you don't do this the insurance company may look the the DMV to see how many licenses are registered under your home address, then they will call and ask if he is insured. so it's better to just go and tell them to add him to your policy.