Many atheists groups already do it, some call humanism, scientism, rationalism other kind of names. And always when churches try to interfer in education for example, they call equality of religion to demand the same space.
even the Flying spaghetti monster church has in the end an objective like this.
And a lot of satanist groups use this name just to opose to christianity butin fact are groups as you define.

Anyway, good luck trying to heard atheists. Without a divine being that gives authority to a priest, it is very difficult to put together people so different, with different backgrounds and objectives.

No need really.

Something about the value of truth. We've struggled with this alot in America.

As such you do have.