30 years ago was a long time ago,

Well with regards to Common Law, the basis of that goes hundreds of years. Anyway, if the 30 years is a problem, over those years I have known several people who have changed their name (after chatting with me) the last was 3 years ago.

As for the same name thing. That of course is not universal. In Spain it is for all practical purpose totally impossible to change ones name and that applies to a woman when she gets married: She keeps HER name.

So far my wife and I, different names, have not experienced any problems in UK (Pension increase: Medical cover provided by NHS for my wife in Spain etc).

If one has changed their name, they should be able to prove who they are, as they have documentation in the previous name and they are the same person; they will have only changed their name. That was what I found when Visa questioned it when I change my name. When I pointed out the obvious that I still the same person who had been their customer for a number of years, they saw the logic.