To turn on anonymous posting in a Facebook group, you must be an admin in that group. Open the Facebook site and select "Groups" from the sidebar, then choose your group. On your group screen, select ...

On this menu, at the very top, you'll see a setting called 'Quick Drop Visibility'. You'll want to toggle this from 'everyone' to 'Only Me' or 'Co-op' if you tend to play in a group.