How does Airport Extreme id computers?

We are in the process of implementing Airport Extreme. Currently, 3 of the 4 Macs in our house are on and have been backed up. The fourth Mac (2007 iMac) has been having some difficulties (unrelated to Airport) during startup and I'm in the process of figuring out if it is a hardware or OS issue. I am concerned that, if I back this iMac up to Airport (using Time Machine) then do a clean re-install of the OS (Lion) or have to get a new hard drive, I will not be able to recover the files from Airport, especially if I change the name or some other setup parameter on the iMac. Is this an issue, or does Airport use something like the MAC address to id the computer?

(I'll probably post the iMac startup question in another forum here.)

The router identifying the computer is for internet addressing only, not for Time Machine. It wont matter what the Airport sees the computer name/address to be in order for Time Machine to recognize it. two completely different addressing schemes. No matter what you name the machine, as long as when you bring up Tim Machine you point it to the backup set you want to restore, it will do so.