You need a reverse proxy - take a look at the HAProxy package.

Note that only applies to web traffic. Not familiar with TeamSpeak but it's not web traffic, I suspect it may be impossible to determine which hostname users are using (unless TeamSpeak embeds that within the packet). If it does embed it, you'll need to write a reverse proxy of sorts that understands that traffic and can pass it accordingly.

What you'll probably have to do is have a unique public IP for each host.