It is back already I believe, if not at least partly. Since I've installed Messenger Plus! 5.0, I've been seeing my own and my contacts' nicknames again.
Come to think of it, looking at my contact list, it seems to be only displayed by people whom I know of have installed Messenger Plus! 5.0 themselves.
Edit:
If you change your Windows Live Profile name, this would allow you to set a custom nickname as well. It's a little less convenient and actually changes your "real name" in your profile, but it is an option.
One way to do this:
-Open Windows Live Messenger
-Press the Alt key to open a menu-bar on top
-Go to Tools > Options.
-In the Personal Information window, click the button "Change Name" behind your current name.
-This will lead you to your Windows Live profile, name changing option page. It will most likely ask you to login prior to this.
-Here it asks you a First and Surname, you can enter whatever you like here.
Certain "unusual characters" will work as well.