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.
That’s what Billy Blythe did—he started calling himself Bill Clinton although he was never legally adopted by his stepfather.