^^ It's called an IP address; all computers have 'em, all poker sites track 'em.
IPs aren't enough. My house has 5 adults, 6 computers behind one router, thereby all sharing the same external IP. And I've logged into sites from 3 different internet connections, meaning my user name has been used by 3 different IPs, some of which have had other users on the same sites logged in. My wife and I have played together behind the same IP at the same time on occasion.
MAC addresses are unique; each NIC has a different one I think, but sites wouldn't have access to that information. Even at that, my wife and I could be using the same computer at different times.
IP is one piece of information, but the name and address on your credit card or whatever you use to make your deposit would seem to be a better one.