Being labeled as an atheist doesn't bother me, I've called myself a skeptic to a few theists but they usually want me to elaborate so they can attempt to challenge my doubts. Often these conversations come at the most innoportune times, I don't have my bearings straight enough to argue. I think they perceive skeptics as doubters who can be swayed and atheists as actually taking the position of denying their creator and precious Jesus. I'd rather cut to the chase. I suppose what would appeal to me as a position or label I'd take on outside of atheism is secular. I would merely take that label however to avoid nasty comments that have been made to me about denying the existence of a deity and not because I actually feel it defines me as a person.
No one understands the use and abuse of the power of labeling better than the religious. "Secular humanist" sounds so cold and scientific. "Atheist" has negative connotations, as does "non-believer".
I rather like the term "Brights", although a bit elitist. We really need a new monniker, something warm and fuzzy.
I think skeptic is probably a better term, because I would say I was a skeptic first and foremost and that is what lead me to be an atheist. An atheist isn't so much who I am but what stance I have on a particular topic.
That having been said, due to the current society in America (and I would assume in other places as well), I would argue that it is very important for people to embrace the word atheist. Other words such as non-religious, skeptic, or agnostic often give believers the impression that we're unsure of ourselves or just haven't thought much about it. Or maybe we still acknowledge God but simply have doubts or something.
It is important to say "I am an atheist" so that people understand that we really mean it, are confident in this matter, and that we are not afraid of stepping forward and being known. I realize that this isn't how these words ideally should be used, but unfortunately it is how they are perceived, and we need to understand and work with that perception.
Hopefully, there will be a day where being an atheist is considered normal and we can start being more descriptive with terms like skeptic and whatnot. Until then, a Christian's mind automatically translates all of these words to "confused & uncertain."