They would go back and change his name based on an adoption that occured later in life? That makes no sense.
It makes no sense, but as God as my witness, in most states....if you are adopted by someone later in childhood, your birth certificate is changed.
IOW, if you are born as Joe McGavin, but are later are adopted as Joe Smith, your birth certificate will officially be changed to say Joe Smith by the state. If lucky, you’ll still have a copy of your original BC.