Attached is a patch against 1.9 that implements anonymous forums as described in the first comment. The patch is incomplete in that it lacks database migration hooks, but these should be simple for a more experienced Moodle developer to add The new columns to support this feature are:
anonymous int2 DEFAULT 0, – 0, 1, 2 = no, yes, optional
anonymous int2 DEFAULT 0
When creating a forum, you can now specify if posts should be anonymous, not anonymous, or optionally anonymous. In the latter case, users are presented with a checkbox that they can tick if they want their post to be anonymous.
Anonymous posts get hidden from the post history on the user's profile, as well as the recent activity block and recent activity full report. When displayed and emailed, the anonymous posts are attributed to the name specified in $CFG->anonymous_name (e.g. 'Anonymous Student'), with current_theme()/pix/anonymous.png used as their picture.
If anyone discovers or knows of other areas where anonymous forum posts would be displayed improperly please let me know.