Is there an extension or setting that let's the user decide if his/her username appears in the logs.
Topic on Project:Support desk
By default, anyone can edit any namespace on a MW wiki (except the MediaWiki namespace which is sysop-protected). Anyone who wants to edit anonymously simply has to log out (if they are signed in with a registered account) then just proceed to edit any page. Their IP will be shown (I am not sure if you can hide the IP other than by doing it manually through RevisionDelete), but no username. Again, some wikis might restrict anonymous editing, forcing them to log in.
Ok, to be more precisely: This is a closed Wiki where users have to log in even for reading and for editing also. If a user has the "Edit" right I want to give him freedom to select if he want to show up his username in the logs or just his IP or something less personel.
Well, I am not sure if MW has such a feature. You will have to wait for someone with more experience about the software to answer. The idea sounds good, so even if it doesn't exist, then it should be implemented.