Do you have to tell your insurance company if someone hits you?

Yes, if you seek to have your car repaired under the collision coverage, or seek other compensation from your own insurer. The insurance policy will require that notice be furnished within a "reasonable" time or "as soon as practicable". These are malleable terms and depend upon the totality of circumstances.

In return for payment under your own insurance policy, the insurer acquires subrogation rights. This means that the insurer inherits your right to pursue the at-fault party/its insurer to recover that which it paid to you.