It's all in the details of the circumstances

• Check in Your Name: In the case of smaller third party property damage claims, IE: If the other party is at-fault and paying for the damage it is not uncommon for the insurance company to pay you directly. Just ask them to issue the check in your name.

• Check in Body Shop Name: Insurance companies will prefer to pay the shop directly when there is a lien on the vehicle (lien holder on the policy).
  When there is a lienholder on a policy, the insurance company must honor the bank's interest in the vehicle by either paying the shop directly, or make the check payable to the lienholder.
• Alternative - Check in the Bank’s and Your Name: When the bank is on the check (even if your name also appears) at some point you will need to get the bank sign off.
  The bank may require a certification of repairs provided by the body shop which can be problematic with out of town banks.
• Thu s, the reason why many companies make checks payable directly to the shop that will certify the work.

• In this scenario since the insurance company has no lienholder to protect, a smaller claim such as this may be made payable directly to the insured.
• It is not my experience that insurance companies cancel collision coverage if you choose not to fix your car. But, they will likely require a certification of repairs and reduce any future claim payouts by the value of the damage that was not repaired. In other words, you can expect that they will not pay for the same damage twice. Adjusters are pretty good at identifying prior damage ;)