Since many users still eschew registration requirements, I hacked the forum.module a bit to allow anyone (anonymous or registered) to use a "display name". This avoids having a lot of posts from "anonymous".
The displayname is stored in the forum database table as an extra column and read in the module together with the real username. If set, the displayname will be shown in the forum pages instead of the username (or "anonymous"). Otherwise, either the real username or "anonymous" will be shown. To do this, I also touched the format_name function in common.inc, which I guess is a bad thing. Anyway, it works...
Anyone interested in my (honestly rather bad) hack?