Yes. While your insurance company may recommend a repair shop, you are under no obligation to take your vehicle there. You may take your damaged vehicle to your own preferred repair shop, and your insurer is still obligated to pay for the repairs. How do insurers pick the repair shops they recommend?
If a Vehicle Repairer Doesn't provide that, or if an insurance company is interfering with your ability to obtain a safe and proper repair, take action. ... It is your car, it is your choice where you vehicle is repaired, by the vehicle repair facility that you choose.