On MSN, just below your name or assumed name, there is a box where you can type a short message that you can change as often as you like. How would you call that if you had to tell a friend you were chatting with : "Oh, I see you have changed your ... ?"
MSN also has an away message in addition to the message in question; this is just a little phrase below the screenname, sort of like a subtitle. For example, my friend's says "Caligula would have blushed" under the likewise mutable screenname, and tomorrow it could say, "ooh la, don peringyown."
To "sig," "tag," and especially "stat," I would probably respond, "What?"
I think "signature" or "signature message" is the best bet.