England and Wales: no, the certificate stays as it was#
No. A birth certificate is a certified copy of the entry made when the birth was registered, and GOV.UK's guidance on correcting a registration says a correction can only put right something that was wrong at the time; it cannot add new information, such as a change of name made later. So an adult who changes their name keeps the same birth certificate. The birth certificate checker shows what your register can do, in two or three questions.
That is not a problem, because the two documents are read together. The birth certificate proves the name you were given; the deed poll proves you gave it up and adopted another; and as long as the former name on the deed matches the certificate exactly, spelling and order included, the chain is unbroken. It is the pairing every organisation is checking when it asks for both.
A baby, within the first year
A baby's first name can be changed, or added if none was given, within 12 months of the registration; the surname cannot be changed this way (changing a baby's name after the birth is registered). The register office adds the new name to the entry without erasing the original, on a certificate from the parents, or from whoever performed a baptism if the name was given then. After 12 months, a child's name is changed by deed poll made by a parent with the agreement of everyone who has parental responsibility, and the certificate stays as registered.
Corrections
A genuine mistake in the original entry, such as a misspelling recorded at the time, can be corrected on application to the register office or the General Register Office, with evidence and a fee. That is a correction of the record, not a change of name.
Scotland: yes, the change can be recorded#
Yes, if you were born or adopted in Scotland: National Records of Scotland can record a change of name against your birth entry, and new copies of the certificate then show your new name and your previous one. NRS says it costs £40, plus £10 for each additional family member applying at the same time, that it does not send a new certificate automatically but explains how to order one once the change is recorded, and that the service cannot be used for a change on marriage, divorce or civil partnership. It is optional: HM Passport Office and DVLA accept a deed poll wherever you were born. Changing your name in Scotland has the detail.
Northern Ireland: yes, GRONI can record it#
Yes, if your birth was registered in Northern Ireland: the General Register Office for Northern Ireland can record a change of forename or surname against the entry on application, and new certificates then show the change. nidirect says an adult can change their forenames once and their surname up to three times, with five years between changes of surname. Recording costs £35, and a certificate showing the change is £15 more. nidirect also lists a deed poll as another way to change your name there.
Can you change your name on your birth certificate after marriage?#
Not in England, Wales or Scotland, and there is no need to anywhere in the UK. Your birth certificate records the name you were given; your marriage or civil partnership certificate is the document that links it to your married name. GOV.UK says you send a copy of that certificate to the organisations that hold your records, and HM Passport Office takes it for a passport in the new name, a double-barrelled one included. In England and Wales, GOV.UK's guidance on corrections says a correction cannot show new information when circumstances change after a birth is registered, and its example is a change of name after marriage. National Records of Scotland says its change of name service cannot be used after a marriage, divorce or civil partnership. nidirect's guidance on recording a change of name in Northern Ireland does not mention marriage either way, so ask GRONI before applying for that reason.
Born outside the UK#
A birth certificate is issued under the rules of the country where the birth was registered, so only that country's registry can say whether it records a change of name. In the UK your deed poll is the document that proves the change, shown alongside the foreign certificate.
