The other driver should be responsible for the damage to your car and their insurance company should be responsible for making the repairs. You might want to inform your insurance company for information purposes and also in the event the other driver does not have insurance and your own policy has to cover it.
Yes, it does not matter where the incident took place. If there's been an accident, you should report it to your insurance company, especially since someone else backed into your car.
The deciding factor in reporting should be the extent of damage, not the location of the incident. You don't state if the driver that hit your car was present and provided their insurance information to you.
If it wasn't your fault, you can file through the other person's insurance to repair any damages. Otherwise, no, you do not have to file through your company.
