At the least, the marriage to Dunham was bigamy by Hawaii statute and the birth illegitimate. By adoption Barry would legally still be Soetoero.His legal signatures and affirmations using Obama would be violations of law.
Not necessarily. There is such a thing as common law name change, i.e., change through consistent usage. It’s actually grounded in free speech. You can call yourself whatever you like. But the rules vary somewhat from state to state, such that a statute can specifically abrogate the power to effect common law name changes. One more caveat. If the name change was not innocent, i.e., was undertaken specifically to hide from a creditor or to avoid deportation, it doesn’t work.