How Important are Character Names?

Names are interesting because there is a history to them and how they have evolved over the years.  Some names are newer than others like Haley, Riley, Tanner, and Hunter compared to Mary, Emily, John, and David.

I find that I don't think about character's names specifically before I begin writing a story, unless a name just fits a character.  Then it's one of those wonderful light bulb moments.  I spend my time developing my characters first and then the name seems to follow.  I think that...