Not. At. All.
My name (Amy) is ridiculously common over here, and has been a major inconvenience on many occasions where I've been confused with or mistaken for a multitude of other people, but I've never thought of it as anything more than a plain old meaningless noun. Perhaps it's because my name is so common and I've known so many different types of Amy's that I feel this way, but that's how it is, anyway.
My name came off a grave stone my mother passed while out walking, so no special significance there. My middle name is Leah, because my mother loved the name Amelia and my father didn't, so Amy Leah was the compromise. I think it sounds like an awkwardly broken up version of Amelia, and that Amelia suits my last name better, so I wish my mother had won that one. I hate the rhythm of my first and last names, so insist on shoving the middle one in there all the time anyway, even if Amy Leah does sound a bit weird. I've considered going by 'Leah' instead of 'Amy' several times, simply because 'Amy' sounds awful with my southland accent and doesn't suit my last name, but eh, too much effort.
I know quite a lot of people who have changed their names, or who go by nicknames all the time, so I wonder if this is the reason why, or if it was for purely surface-level reasons of not liking the way it sounded, or something. Varies for person to person, obviously, but now I'm tempted to ask people...