Surnames, and changes after 12 months
The register office can’t change a surname just because you’ve changed your mind. A birth can only be re-registered with a new surname in particular situations, such as adding the father’s details or after the parents marry. Coram Children’s Legal Centre lists them. Coram Children’s Legal Centre: changing a child’s surname
For anything else, including a first name after the 12 months, use a child’s deed poll. It can change any part of your baby’s name, first, middle or surname, and the birth certificate stays as it is. You show the two together whenever you’re asked for proof of the new name.