Again, that depends on the state. The majority of shops that I know in Louisville would not keep a record of the transaction other than the reciept needed for business purposes. No federal registration would occur, and the state should not be concerned with each individual transaction as long as the taxes are getting paid. But, yes, that would technically be a paper trail. If you paid with cash and scheduled the check where you could wait while it was performed, there would be no reason to give a correct name, if you were even asked. If you are that concerned, I would strike up a conversations with knowledgable gun owners and ask for a recommendation for someone to perform the maintenance check privately. My guess is that you will easily able to find someone, as this is not illegal and no one will susupect that they are being set-up.