At The WELL in the 1980s our policy was you had to use your real name. We only allowed a couple of exceptions. But that society was when online conversation was new and trolling as a sport hadn’t happened yet. Plus the atmosphere of the WELL was heavily influenced by a certain “Whole Earth” ethos that helped the initial tone of the place get set in a pretty civilized direction.
Later when it got bigger and things got more socially complicated, we did allow some people to mask their real name online but we still had to know who they really were so that we could bill them (there was a monthly and an hourly fee back in the modem days) and so we could make good on our “you own your own words” rule that was less about copyright and more about the poster taking responsibility for whatever they said. They system overall worked pretty well, and at that time I was in the camp of mandating the use of real names for just about everyone.
Then in the mid 90s when I started a conference-like system for SF Gate, at first I made everyone use their real name. That went ok for awhile, but then one weird guy started to stalk offline a young woman who was one of the most prominent users of the system.
That caused me to change it so you could mask your real name but we did mandate that you had to have a persistent user name so whoever you called yourself developed an identity around that name. This is the “stable pseudonyms” that jamescookmd is talking about above.
If I were designing a system now, I would still opt for the stable pseudonym model.
One of the great things about the online world today is that there is such a huge number of offerings with every kind of style imaginable, that whatever model one chooses, someone can easily go someplace else to have their say. There is no one way to do it that solves every problem.