I didn’t.
When I was in my late teens / early twenties I told my boyfriend, now husband, that I intended to change it. But over time I grew to dislike the idea; it just seemed like a) a lot of effort and b) entirely pointless. My husband had grown attached to the idea of us sharing a name, which I respected (he did not attempt to make me change it, he was just being honest about how he felt).
So I was a bit conflicted; after all it was my name, I shouldn’t feel guilty about not changing it, especially since it’s not even a tradition in many countries. I proposed a compromise: that I would be “Ms maiden-name husband’s-name” socially and “Ms Maiden-name” professionally / in all other respects.
However, a double barrel surname is a MASSIVE HASSLE; the moment I realised that it wouldn’t work was when I rang a restaurant to make a booking and gave my “social” name. When I got to the restaurant, they couldn’t read my name on the booking because they had smashed my 2 surnames into one “surname” box on the online booking system

And that is fair enough; not many people have 2 surnames.
So, now, basically I just have my facebook profile as “first-name maiden-name husband’s-name” and use my maiden name for everything else, even though I have moved to the other side of the world so any friends I make will find it hard to add me on facebook because they won’t know about my double barrel facebook name. I can’t really change it back though; people would read into it.
I can see 2 reasons how it might be hand to take your husband’s name: it might be handy to have the same surname when you have kids. The other reason is if you rally hate your maiden name and your husband has a suave surname
Also, while I of course accept that it’s understandable that people assume that I would take my husband’s name, I do find it slightly strange that people call me “Mrs Husband’s-name” when I never indicated that I intended to change my name. Though I don’t bother correcting people, because there is a lot worse you could call me
So, that is my story, sorry, it is very long. Tl;dr, I didn’t, women should just do whatever they want re: the name change thing, it’s just a tradition and there is nothing wrong with breaking OR keeping archaic traditions.