You'll have to register the software on each computer that you use, using your personal User ID and License Key. Two things to keep in mind: (1) Are you following the license restrictions (see
http://www.thetournamentdirector.net/faq.html#faq1)? The licensing is pretty lenient, but you should always check. (2) Unless you uninstall the software, your User ID and License Key will remain in use on that computer. That means even though you unplug your USB memory stick (and thus "remove" the software from the computer), if someone comes along and installs the software on that computer, it will already have your User ID and License Key in place. If you want to remove your User ID and License Key, you'll have to remove the following registry keys:
HKEY_LOCAL_MACHINE\SOFTWARE\The Tournament Director 2.0\UserID
HKEY_LOCAL_MACHINE\SOFTWARE\The Tournament Director 2.0\Key