I just found this on the CAB website but am a bit confused as to what it means:
A man registered on the birth certificate as the father of the child has no right to insist that the child is given a particular name, for example, his surname.
I think that means when registering though not afterwards. And also this one:
This means that where the parents are or have been married, neither can change the child’s name without the consent of the other parent. If the parents have not been married, the mother can change the child’s name without the father’s consent unless he has acquired parental responsibility through agreement or by a court order.
Anyone shed any light?