If you didn't follow ice-hockey, would you bother about what kind of "non-fan / un-fan" you were categorised as? It would be a non-issue, as I suspect this is.
Those (if there are any) who worry about their particular atheist label are possibly not atheists at all, but people going through a Lewisian 'angry-with-God' phase; like a die-hard hockey fan who has sworn off hockey
for ever over a defeat for his (or her) team, the strike, or some such thing.
Having said that, I don't like the 'brights' idea. It sounds silly, for a start. It's also depressingly reminiscent of a problem with the
Humanist Association; being about 'joining' - manifestos and commmittees, subscribing, defining, signing up to statements you didn't think up yourself, appointing officers... a herd mentality that's a mirror of religious hierarchies and dogmas.
Atheism should be an ill-defined and individual idea; people thinking for themselves and linked by no more than the perception (or suspicion) that the religious emperor has no clothes.