My wife didn't change her name when we got married. She really didn't care one way or another, but if I asked her to do that, she would change her last name to Brown, as compared to her last name A.
Now, I see a woman's last name as her main identity. She has had her same last name for 46 years before she met me. Some other friends who have married have done what "their generation" did -- just change their name "just because" that is what you should do (much like you should have children "just because"). One friend changed her name because she did take the name of her husband -- who ended up being a control freak and lazy, cheating SOB. Thusly, she had a very bad association with that name. When she got married to her current husband, she gleefully changed her name.
I've heard the explanations -- that changing her last name makes her feel more at "oneness" with the relationship, that it is a symbolic "giving of everything" to her husband, things like that. It sounds like force-fed programming that girls receive from their mothers, their friends, and society in general so that they will be "proper women" when they grow up.
My wife has an fairly uncommon last name. She is proud of that name. In addition, I want to see her as an equal in our marriage relationship. By changing her name in my mindset, would mean that she would be "less equal of a person" in my eyes. However, if she insisted on changing her name to mine, I would not stand in her way.
As a man, I never understood that tradition. It seems demeaning to me by making women, who become wives, willingly ...submissive... by sacrificing their last names for the relationship. I understand that it is an individual decision, but it seems to be a decision that is made for them by society, especially for older women.
As for how my wife handles it, she knows that people, who don't know her, will call her L Brown, or Mrs. Brown, or she'll get mail addressed to L Brown occasionally. It's a fun game -- if there is mail addressed to her as L Brown, versus L A, I kid her about it and say "Gee...I didn't know you changed your name.

" It really is not a big deal for us.
Overall, the changing of a woman's last name when entering a marriage is a decision I accept, but I just do not understand -- nor do I think I ever will.