Wow!
Thanks everyone for your help.
I fell into the trap I warn other people not to, and that's to assume a name added to a 1939 entry is a marriage! I knew that it couldn't be as a result of her mother's re-marriage, otherwise her mother's name would have been amended too, and anyway, my research had already ruled that out. I never thought about adopting another surname element, and I must admit I haven't looked at her maternal side much at all, something I will now do, focussing rather on the Hollands. I had spotted the references to
Miss on the passenger list and in the London Gazette, and must admit to being a bit confused about that, but I am well aware that sometimes married women prefer not to use
Mrs. It does seem, however, that the
Lambton part of her name is something she adopted herself. One day I'll make a note of the 1939 register codes and their meanings

I have contacted (eventually, after my initial email bounced as the email address on their website is wrong) the Ripon Gazette about Barbara's obituary, and await their reply. I will follow up the suggestion about contacting Ripon Grammar. Thanks to
arthurk for the magazine cutting - the only other I could find was on FindMyPast's newspaper search.