Unless you live alone and don't permit anyone else to use your car for business or pleasure, it's unlikely that your auto insurance policy is a true "single-coverage" document. Unlike a health or life insurance policy, your auto insurance policy probably contains several "implicit coverages" that are already factored into its cost. In fact, U.S. law requires auto insurance companies to extend coverage to certain other licensed drivers with whom their policyholders might interact on a regular basis. These provisions exist to protect individual policyholders from being held liable for incidents that occur without their knowledge or consent. However, they don't necessarily absolve policyholders from financial or legal responsibility for the actions of implicitly-covered drivers.
In practice, these provisions are enforced at the household level. If you own a vehicle, every non-dependent licensed driver who lives in your household must be included on the policy. If you share an apartment with three other licensed roommates, those individuals will be listed as "occasional drivers" on your policy. You'll be responsible for manually adding these individuals to your policy. Moreover, your insurance company will hold you accountable for doing so.
If you fail to mention on your policy application that you live with other licensed drivers, any claims related to their actions as drivers could be denied. Worse, your insurer could choose to drop you from coverage as a result of such a misrepresentation. Since failing to report the presence of other licensed drivers in your household technically constitutes insurance fraud, you could be held criminally liable for your actions. You might also face a private lawsuit from other parties to the accident. The licensed housemate who actually caused the accident is likely to be named in this suit as well.
If you're looking to add a dependent child to your existing auto insurance policy, you'll need to do so manually. Since it may cost a substantial amount to add a newly-licensed driver to your policy, you should think about the consequences of this course of action. Depending upon the terms of your policy, adding a teenage driver to your policy could raise your premiums by $800 to $1,500 per year.
If you wish to add a licensed adult driver who doesn't live in your household, your costs will be substantially lower than this amount. You'll need to specify that this person is an "occasional driver" who doesn't live with you. In addition, you'll need to make sure that he or she has non-owner auto insurance before turning over the keys to your vehicle.