Are you serious? Think "Haley's Comet," and not some over-the-hill English actress who starred in Disney films three or four decades ago.
Names do matter in politics which is why I knew GORE would not win. But a first name of Haley is a girl's name and an impediment to the presidency? No way. I'll grant you some "modern day parents" have taking to naming their girls Haley, but they've not hi-jacked the name to feminism entirely.
His full name is Haley Reeves Barbour, and I'll bet that were he a democrat governor, many babies would be named after him. Heck, some smart parents still might.
Now, I'll grant you we'll not ever elect a president or a mayor named walkingfeather. :)