You should re-register your child after marriage. Details can be found on 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.
Any correction requested to a birth certificate will have to be accompanied by a non-refundable fee of £75 or £90 (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. We therefore request that you check the register page very carefully before signing to avoid the need to make corrections