Giffords had already been elected to a few terms in the state legislature and to at least one term in Congress when they got married, so I figure that she decided to keep her maiden name with which she had run all of those campaigns and run all those ads. To each his own.
I wouldn’t say it means nothing. The American or Western tradition is for the woman to take on her husband’s surname. Whether this good, bad, or whatever, is not the issue. She choose the non-traditional method that states her own importance.