Not always anymore ... One of my good guy friends took his wife's last name :) it's just traditional, and some people like tradition. It's not a must or given anymore.
Why is it when a woman gets married her last name changes?
It's been this way traditionally. I have no idea where it started to be.
But today, in many countries mostly the west region is not the same thing anymore. In U.S you can choose whether to change your last name to your partner or keep yours. As Jaimie said, even man can get woman's last name instead.
It's traditional but is no longer universal.
---
Maiden Name by Philip Larkin
Marrying left your maiden name disused.
Its five light sounds no longer mean your face,
Your voice, and all your variants of grace;
For since you were so thankfully confused
By law with someone else, you cannot be
Semantically the same as that young beauty:
It was of her that these two words were used.
Now it's a phrase applicable to no one,
Lying just where you left it, scattered through
Old lists, old programmes, a school prize or two,
Packets of letters tied with tartan ribbon -
Then is it scentless, weightless, strengthless wholly
Untruthful? Try whispering it slowly.
No, it means you. Or, since your past and gone,
It means what we feel now about you then:
How beautiful you were, and near, and young,
So vivid, you might still be there among
Those first few days, unfingermarked again.
So your old name shelters our faithfulness,
Instead of losing shape and meaning less
With your depreciating luggage laden.
Because at one time women were considered property. They had no rights. Thankfully, in most of the developed world that has changed. Nowadays a woman doesn't need to take her husband's name. Or they can hyphenate their maiden and married name. I was going to do that, but it wouldn't fit on a driver's license at the time I got married. They have updated that now.
Feelings are different for different ages and different stages. Let me explain.....
When I was younger I wanted to be Mrs. Yang because I wanted the world to know he was mine. Hands off! LOL! By the time we finally got married, I kept my maiden name cuz I thought it would cost too much money for me to change it. (Naive silly me!) Then when I was ready to change it, I once again didn't because I thought I was betraying my dad. See he only had two daughters and one had passed away so I felt I needed to keep my maiden name to honor him since I was the last one. Then it became a convenience having separate last names. (Please don't ask! LOL!) But it bugged the both of us that my last name was different so for our 13th wedding anniversary I wrote him a poem, read it and handed him a "jewelry" box. When he opened it, it held my new social security card.... With his last name on it. :0)
It is a traditional thing. I believe it was some sort of "possessive" description. You were Miss Smith now that you married Mr. Jones you are now Mrs. Jones. In many countries they use another form which loosely translate to "of". So Miss Smith would become Mary Smith of (belonging to) Jones
Dear Megan Goodgirl,
In some cultures the custom is matrilineal...for example when I went on a canoe excursion down the Green River around 1990 in the American Southwest, we discovered some Native American tribes the name passes through the woman's family.
The husband even goes to live with his wife's clan, and the old wise women of the family make the decisions. That got strange in the early part of the twentieth century, women would try to borrow money to improve the land but banks lent only to men then! She would say "But I own X hundreds of acres and cattle"... Or whatever...as collateral for the loan... But no, not until bank guidelines changed!