AirPort Utility 5.6.1 for Windows disallows entering dots ('.') in the global hostname. Whenever you try to enter a '.', it just beeps with an error.
Setting a global hostname is the AirPort way for the "Dynamic DNS" feature found in other routers; i.e. a way to register a hostname for your dynamic IP. It can be found by clicking the AirPort button, then going to the Base Station tab and clicking the Edit button by the AirPort Express Name field.