You cannot pay for a white label subdomain. You can however license the engine for internal use only (but pricing makes it only make sense for large institutions).

citation: http://meta.stackoverflow.com/questions/16054/is-the-stack-e...

It looks like at one point, they did used to offer whitelabels:

http://meta.stackoverflow.com/questions/83591/how-to-run-a-p...

Sorry I couldn't find a better link on short notice :)