With the introduction of NHS Covid Passports, it is very important that your GP record and your Passport have the same name. If you are updating your GP record with your married name (or for any other reason), please ensure that you also change your Passport (and other ID such as driving licence) too so that both records have the same name.
This will avoid confusion at the borders when travelling, or any other time when you need to provide your identification and NHS Covid Passport.