I would argue that in our culture a woman's first name now personally defines her equivalently to how a man's last name defines him.
I'm listening.... This is when you present those arguments.
A man's last name will always stay with him. A woman's last name will change with marriage. And yes, I'm aware that marriage and is a choice as well as keeping/abbreviating/hyphenating a maiden name is. But her first name will never change, regardless. In the case of Hillary Clinton, Bill Clinton is the one most associated with the name "Clinton." Hillary is using her first name as a way to make herself more recognizable as an individual away from the Clinton name. This is the point that I am trying to emphasize.She also uses her first name to distinguish herself as an individual from her husband, who is also a politician.