The “group chat is not anonymous” feature that Converse shows means that people in the group chat can discover each-others JIDs.
You can toggle this feature by re-configuring the room. There are a couple of ways to do this. In the Openfire Admin Console, you can go to the room (Group Chat > Room Administration, select the room) and change the value for the “Show Real JIDs of Occupants to” option.
How do you see that messages are not logged? Do you do search for keywords and nothing comes up? It usually takes a while before new messages appear in search. You can try updating to 4.3.2. You can also try rerunning indexing on the monitoring settings page (archiving).