We've made a few private forums for local this and that.
Two important things are, any account is required to meet the Real Sounding Name Policy
https://permies.com/name.jsp and behaviour follows the
Be Nice rule everyone agrees to when making an account.
Moderators can see private groups, but we generally ignore them unless for some reason we don't. - deliberate vagueness to hopefully cover all eventualities.
One thing I find useful for local groups, especially with buy-and-sell kind of situations is to lock the
thread (staff have this power, but the group manager can signal when it's time to do that) and it sinks to the bottom while still being visible in an archival kind of fashion.