I'm confused...?

I always thought that a woman, when she married, would take the surname of her husband unless she opted to keep her maiden name, or hyphenate. Also my mom goes by her first, her maiden name in place of her middle, and my dad's surname as her last. Well, recently I noticed in legal notices, or obituaries, women would be listed as First, Middle, Maiden, and Married Name. Can anyone explain this to me? I am engaged, and my fiance' and I would both prefer for me to take his name, but I don't understand the aforementioned concept.