If you are a mother it is likely that your child has the same surname as their biological father. But what happens if you separate from their father and at some stage wish to change their surname (or the child requests this change)?
First of all I would advise you to think very carefully about this. Is if fair to take away from your child their link to their father through their surname? You need to consider the pros and cons of doing so before you go any further.
The good news is that if a child is aged 16 or over then they can proceed to change their name and parental consent is not required.
However, for children under 16 years, if their father has Parental Responsibility then you will need their permission. A father will have Parental Responsibility if they are or were married to the mother, if their name is on the birth certificate and (for England and Wales) if their child's birth was registered after 1st December 2003 (or for pre 1st December 2003 births where the father's name is not already on the birth certificate, if they re-register the birth with the child's mother), if they have a Residence Order in their favour or a Parental Responsibility Order relating to the child or both parents have signed a Parental Responsibility Agreement.
If the father has Parental Responsibility then the first step is to seek his permission. If he consents then he can sign a change of name deed (usually prepared by a Solicitor) which you will also sign and then certified copies of this can be sent to the Passport office, your child's school etc.
If he does not consent then you would have to consider making an application to Court for a change of name. The Court will not automatically change a child's name, in fact Judge's prefer to retain a child's original surname, unless there are good reasons for changing it.
Sufficient reasons may be the father not being involved in a child's life (perhaps due to his disinterest or the Court or Social Services not deeming it safe or in a child's interest for him to have any involvement), or concerns as to the child's welfare due to their association with his surname may be enough, but this will very much be down to the Court and the Judge.
The Court will have to carefully consider the effect of severing this tie with one biological parent.
The Court could consider that either inserting your surname before the original surname (or afterwards) or double-barrelling the surnames may be a reasonable compromise. Of course, if may be worth proposing this form of compromise before this goes to Court.