Can i choose the accident repair company if the accident is other driver's fault?

There are a couple considerations:

Yes you can if:

• The shop you chose is not baned by the paying insurance company
• The insurance company approves the repairing shop
• They repairing shop will do the work for the money provided by the insurance company

OR

• You are willing to pay the remaining amount the insurance company wont cover. I have done this to get a shop I trusted but wanted "To Much Money" for the repair.