Renameuser
Renameuser is an extension that lets the administrator of the wiki rename users, even themselves, a feature that does not exist in MediaWiki unless this extension is installed.
Of course, that's not saying that someone with a MediaWiki install CAN'T rename users. If you have web server access and/or a program called PHPMyAdmin (which allows you to mess with the database directly), you can go into the database structure, find the users table, and rename users from there, but this can be tricky, may not cover everything (like, say, if you wanted all the contributions of the previous username to apply to the new one), and speaking from experience, you shouldn't edit the database directly unless you have some idea what you are doing.
So this extension is a far simpler, safer, and saner way rename user accounts without a serious amount of risk, not to mention it's a lot simpler and easier to use.