Well, I don't think MAC Address is all the way out. Sure you can spoof yours, but if there is a super-admin out there who knows all of the MAC addresses that are supposed to be on at any given time, or at least how many MACs are supposed to be on at one time, then the admin could tell if there are any extras.
As far as telling who it is exactly, I am not sure how to do that. Most Wi-Fi routers act as DHCPs, so IP address identification would not work. Maybe if you could somehow limit the amount of IPs assigned by the router, you could prevent any other from accessing the network that way (unless one is being unused).
I think that to get the persons name, you would have to counter-crack their machine once it accesses your network and search for some kind of registry or identification.
Makes you think about how anyone could get caught wardriving...
Thoughts determine what you want,
Actions determine what you get.