Yes, most insurance companies will require you to continue to have your licensed child listed on your auto insurance policy as long as they live in your household, even if they are 18 or older in age. Usually your insurance carrier will want all licensed drivers dwelling in a residence listed on the policy.
Many insurance companies will require that a son or daughter that is away at college but returns home for breaks and the summer remain on the policy as well since he or she will likely drive the family car(s) when home visiting.
To find out what your insurance company mandates, since insurance companies guidelines can differ, contact your insurance agent. To find out if there are any specific state insurance laws governing this situation you can contact your state's insurance regulator.