That's an interesting question. There is something to be said about our history as gay men and women. No, we don't have to use those hidden terms any longer, but I don't think many gays look at themselves as "closeted", nor use that term to hide who they are now.
I think it's more of a rite of passage for other gays, and maybe they are proud to use it.
If we did change the FOD...what would we call ourselves? Personally, I would like one that incorporated gay women and transgender too, not just the gay men.
BTW, "Friends of Bill W" is another clandestine name and they meet regularly. Personally, I like "Friends of Dorothy" and have no shame, closeted feelings or otherwise regarding them.