Your community is based on real-life acquaintances between people who've gone to school together. I would suppose it's the real identities and the real connection those people have with each other (good and bad) that makes the online interaction worth cultivating in the first place. Take away that sense of identification between them by allowing anonymous members to stay hidden behind fake names/screen names, and I think you will make the openly identified people uncomfortable, wary, and suspicious of other members in the group. But those are folks you want to make feel welcome and comfortable, so that would hurt the open/relaxed atmosphere you're trying to create for them ... and they're the ones who'll participate actively in this kind of group so they (should) matter most of all.
If you allow people to register as full members who don't wish to reveal who they really are by allowing anonymous usernames, then you're indulging the wrong crowd who are much less likely to contribute to your community in a positive way.
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