I don't know whether this has already been covered in another thread, though I haven't seen it. The French state has decided that all Covid vaccination and test certificates must be issued in the birth surname. This name appears on French IDs and Passports but for anyone travelling to UK on a UK passport who has a different surname from that at birth there will be a difference. UK.gov says the names must match. This caused a moment of panic for my wife travelling back yesterday after getting her Antigen test certificate. I rang Ouistreham who said it is not a problem, so long as the date of birth is and forenames are correct. However, I did note that if both surnames have been given, then if you are sent a link to download a copy of a test certificate the page preceding download shows both surnames and lists tests that have been received. We screen shotted this and printed it to staple to the certificate (belt and braces).
I hear that many airilnes insist on a marriage certificate and some will not accept a mis-match at all.
Incidentally, it appears that HMG has completely outsourced the checking of documentation and at Portsmouth they only want to see passports as they can see on their system that all Covid status has been checked. At Cherbourg last night the process was extremely lengthy. Despite 1.5 hour checkin, they were still checking in up to departure time and many cars were parked up with drivers in the terminal trying to get their documentation in order.