What surname will the baby have
Choosing your child's surname
Your child can take the surname of either parent, or both. Even if you are not married and the father doesn't attend the birth registration, you can still give your child the father's surname.
Changing your child's surname
The following link may be useful: Change your name by deed poll: Change a child’s name - GOV.UK
There is no provision to change your child’s surname as part of the re-registration process, your child’s surname will be recorded as it is in the existing birth registration.