There is an input field in your user Preferences (in the Signature section, down the page). You can use that to specify a unique nickname to be displayed as your signature instead of your registered account name. This field may also be used to custom design your signature with wiki markup (check the box labeled Treat the above as Wiki markup).
Whenever you sign a post with ~~~ (nickname only), or ~~~~ (includes nickname and timestamp), your new nickname or wiki-markup will be used. Bonus tip #1: ~~~~~ (timestamp only).
Bonus tip #2: To display a nickname, the software adds [[User:Name| to the beginning of the nickname, and ]] to the end. So, by entering something like Klaaus Meieer]] [[User talk:Klaaus Meieer|(talk), you can "trick" the software into adding another link at the end, in this case, to your talk page, which will look like this: Klaaus Meieer(talk).