After a car accident, you would have to get your car repaired if it can still be fixed. You have the option to have your car repaired at any body shop of your choice.
Auto insurance companies have contacts of body shops in the area. Insurance companies will benefit from you choosing from their list of body shops where they have negotiated discounted rates for materials and labor. One of the benefits of having your car repaired in their chosen body shops is these shops already passed the requirements set by the insurance company, making processing of paperwork smoother and faster.
However, you also have the right to have your car repaired in a body shop you know and trust if you do not feel comfortable in any other. Your auto insurance company should still handle all the requirements and coordinate with your chosen body shop. It is highly likely that auto shops who are not part of the recommended list of insurance companies will be willing to process your repairs.
Whichever you choose, understand that it is your choice and that your insurance company will pay for it no matter which body shop you go. Your insurance company may try to convince you to bring your car to their chosen body shop. Do your own research on the body shops in the list of your insurance company. It would also be beneficial if you ask people you trust which body shop they bring their cars to. This way, you already have an honest feedback, and will be more at ease that your car will be repaired to the standards that you want and deserve.