That's the computer name. It's different than the client ID. It's not used for DHCP or TCP/IP in any way, shape, or form. If you go to TCP/IP properties, and click on the DHCP tab, the Client Name is what is really used for TCP/IP and DHCP stuff. The machine name could be "Fred", and as long as the Host name (in the TCP/IP properties) matched whatever your DHCP server needed to see, you'd be fine. The thing is, though, that the Machine name and the Host name usually match, and Windows will warn you if they don't, so it can appear that the machine name is used for DHCP configuration.
To clarify, this is how it works for Windows 95, 98, and NT 4.0. I have not really worked with any flavors of 2000 or Me, so I do not know if they've changed it.
-otherguy