A common misconception. You can legally call yourself anything you want so long as there is no intent to defraud. BHO certainly had a legitimate reason to go back to his birth name which he held until he was adopted by a man who subsequently was no part of his family. It would not legally nullify any acts he took after re-assuming his old name.
Meanwhile, all the identity documents he is currently using amount to fraud if he ever uses them in court or to obtain services.
Social Security Number (issued in Connecticut)
COLB (proven fraud)
Selective Service Registration (proven fraud)
Why did he give up his lawyer’s license? ‘Tis a tangled web, woven.