I am happy with the term ‘atheist’. Since most people are theists, ‘atheist’ is both necessary and perfectly defines us. It might give too much credit to the theist position, but that’s impossible to avoid. ‘Brights’ was an attempt to coin a term that put us on equal ground with theists, but atheists are a tough bunch to rally (herding cats is often heard when trying to do so), so it was a short-lived experiment that fizzled out with no one noticing. Also, with a new/different term, you’d have to define it to people all the time, and that makes you look like a weirdo creating a special name for yourself.
Saying your an atheist lets people know you’re not ashamed of the fact you disagree with the majority of people. I’m a quiet and friendly person, and when people find out I’m an atheist I am often the first one they’ve met (they’ve obviously met many, but I’m the first to tell them). Since I’m polite and have an honest interest in discussing different beliefs, they inevitably leave with the fact that atheists are decent people and not SJW’s or militant or Satanists.
If you give the term ‘atheist’ a good name, it will get a good reputation.