If you'd like to post something in a Facebook group without revealing your name, use Facebook's anonymous posting feature. It's easy to do, assuming that a group administrator has enabled the feature.

We’re giving Facebook Group admins the option to change their group from private to public while still protecting the privacy ...

Often, admins start their groups as private, thinking they will remain small, but then realize they could reach a much ...

A Facebook Groups update that would now enable administrators to make their previously private groups public without ...