I think men and women grow up with different perspectives on, and attachments to, their surname.
For men in the West, it's an inheritance, something fixed and unchangeable and weighty – a line that connects them back to generations of male Whatevers. They come to embody the House of Whatever, its class position, its ethnic composition, its glories and shames. Surnames have a particular authority for boys. Men, especially the most privileged and successful – public schoolboys, athletes, history makers – are known by their surname alone. Footballers have it written on their shirt. It's possible to leave school without knowing the first names of Gladstone or Gandhi, but not so for Nightingale or Stopes. To some extent, a boy's surname is his brand.
That's not so often the case for girls. We grow up more aware that we're the descendent of lots of different surnames. The role models we're presented with in the mainstream media are often known by their first name, or a nickname: Kylie, Twiggy, Sam Cam, Serena, Hillary. The given name is the part of our name that is sure to be permanent, and also the one that displays our femininity. Surnames are thoroughly coded as masculine, not just linguistically (think of all the Jameses and Johnsons, surnames linked to male labour, surnames ending in -man and -son, etc) but also culturally: if we overhear someone talking about "Smith" or "McTavish", we assume they're talking about men.
In that context, I don't think it follows that the feminist choice is always to keep one's birth name. My attachment to my surname is not significant. I have a hard time accepting that, because men are attached to theirs, so I should be to mine.
I do, however, think it's a feminist choice for men to take the surname of their wife-to-be. The question, in my eyes, should be: why are so few men prepared to do that?