The tradition of the wife taking her husband's last name at marriage is not found in the bible. It didnt exist back then. It's a relatively modern invention. Back then women were defined by where they lived, who their kids were or who their husband was but last names simple did not exist. The bible issues no command for a woman to change her last name - therefore the notion to do so isn't biblical. Its cultural.
In western society women continue to change their names for personal reasons.
It should be noted that popularly people illustrate their union based on what you said, two flesh, man and woman becoming one, since the man was the head of household it was his job to nurture her and therefore the woman would take the husbands name.
And while most intentions start out pure-- and many remain so, it cannot be ignored that over the years a once innocent proposition became bastardized. I'm speaking historically here of course. This is in no way currently relative.

I am not a feminist. I'm actually, personally, against modern feminism .. for like you mentioned-- it has been hijacked. However, one doesn't have to look too far to find where the insinuation of ownership around a married woman is woven tightly into our history.

I do want to thank you for commenting! Genuinely! I agree with you on the hijacking of feminisms and religions like islam being incompatible with western civilization. And please don't confuse where I am coming from here, I am not demonizing all marriages and the taking of the mans last name, however, I am not ignoring that once upon a time women had no rights, no money, couldn't drive a car or be held responsible for more than running their home. We've come a long long way, and women are no longer viewed in such limiting capacities anymore which is why I don't actually understand western modern feminism. But I'm not going to ignore history as well.

The last name portion was just a teeny tiny part of that post though. I hope the rest wasn't lost on that difference of opinion.