I think, something like...
update minibbtable_users set username='NEW_USERNAME' where user_id='USER_ID';
update minibbtable_topics set topic_poster_name='NEW_USERNAME' where topic_poster='USER_ID';
update minibbtable_topics set topic_last_poster='NEW_USERNAME' where topic_last_poster='OLD_USERNAME';
update minibbtable_posts set poster_name='NEW_USERNAME' where poster_id='USER_ID';
Substitute 'NEW_USERNAME' for the new username you want to appear, and 'OLD_USERNAME' for the current name. You must know 'USER_ID' in advance. Hope you know how to do it :-) [roll over cursor on "Member" title and you'll see something like ....action=userinfo&user=USER_ID ]
I think, if you'd have private messages add-on, it's much difficult to change username in it's storage files... a special script is needed for changing usernames. But on another side, it's not really necessary it to do it for some kind of "mailing" program... It's kind a separate script.