Just to point out that either partner can change their name when they marry.
But if a wife takes her husbands name the marriage certificate is the only paperwork needed. The other way it's deed poll time (not that that is especially difficult).
I don't believe that's the case any more. It was when I got married in 2016, so I left it, but I need to renew next year and it's no longer the case, marriage certificate is enough for men too.
You appear to be correct, Co-Op legal services say the process is the same for a man with key government departments, eg the passport office. I don't think it was when I got married last millennium but IANAL.
But if a wife takes her husbands name the marriage certificate is the only paperwork needed. The other way it's deed poll time (not that that is especially difficult).