A person is registered at birth as Brown. He is brought up believing his name to be Smith. He has a son whom he registers as Smith. He then finds out his true surname and changes it from Brown to Smith by deed poll. What surname should the son have.
The name on his BC until he's old enough to change it by deed poll if he wants to. You don't have to go by the name you were given at birth. You can inform schools, doctors etc what your preferred name is. As long as you're honest when asked 'have you been known by any other name'