[Digital Jedi]

If I were trying to do this, I wouldn't necessarily go the modification route. I'd force the particular forums I wanted this to happen in to use a specific style (which you can do in the Forum Manager). Then I'd customize the appropriate postbit templates in that style by stripping out username or Identifiable info, depending on how anonymous you want them to be (i.e. stripping out anything that might display a user ID.) Then, in the main style your forum uses, I'd use an IF condition around the appropriate code in (I believe it's) forumdisplay to exclude the username/lastpostby based on that forum ID(s). Which would effectively remove user names from that forum when showing up on forumdisplay.php and New Posts.

A little bit of work, but not necessarily difficult work. And it's safe enough to experiment with the custom style first yourself, before going live with it.