State insurance laws and insurance company guidelines vary but in general if you live with your dad you will need to be placed on his policy as a licensed driver in order to be properly covered. Most insurance companies require that all household members and/ or drivers be disclosed.
State laws do not typically require a person to notify an insurance provider of a child with a license. It is likely though that the insurance company has written into dad's policy that he needs to inform his agent of all licensed members within the household.
If you do not reside with your dad but visit or borrow his car often, then he should inform his insurance company as well. They may want you to be added as a driver or an occasional driver in order to be covered by his insurance coverages.
Since insurance companies guidelines differ the best way to find out if you will be covered by your dad's insurance policy when driving his car is for him to call and explain how often you drive the car. The insurance agent should then be able to tell him if you need to be added to the policy or what coverages you have, if any, without being added on.