How will the insurer issue the check to repair my car?

It depends on if you're in a first-party or third-party claim situation. When the claim is being paid by your insurance company (first-party situation), a check will likely be made out to both you and the repair shop. When the claim is being paid by the other driver's insurer (third-party situation), the check will probably be made payable to you alone.

For further explanation, see who gets the claim-payment check?

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