You should re-register your child after marriage. Details can be found on Application to re-register a birth following marriage or civil partnership of the mother and father - GOV.UK as to how you do this.
For corrections to a birth entry, please contact the register office you attended who will advise you on what to do next.
A non-refundable statutory fee of £83 or £99 will need to be taken for the correction to be considered. This is dependent on whether the correction can be done locally or has to be referred to General Register Office.
Any correction application must be made in the district where the event occurred with the completed application form and relevant evidence. We therefore request that you check the register page very carefully before signing. Once the page is signed, the entry is a legal record of the registration and cannot be changed without completing the formal correction process.