Shoutbox

See Tabbed Chats - wrong contact.
In the same thread you will find a script called Tabbed chat taskbar button changer by CookieRevised

Alternately if it's just that you are afraid of missing a new conversation started with you, you can set a notification for "started new chat" as shown in the image below:



You can even set it to play a sound in the same event notification if a visual notification isn't enough