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.
Facebook has unveiled a new feature: group nicknames. Know what it is and how it works.
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Facebook adds nicknames in Groups to take on Reddit

Facebook is rolling out a new nicknames feature in Groups that lets people post under an alias instead of their full profile name, a clear attempt to capture some of the pseudonymous culture that has ...