You can find your computer's name on a Windows PC by opening the "About" menu, and on a Mac with the "Sharing" menu.

If you want to give your Mac computer a new name, the process is easy and can be completed in three steps.

I need to take a running windows desktop box that's part of a domain, give it a new computer name, and then continue working on it (with the box having the new name), without having to reboot at all.

From looking at things, it might be a Win7 difference on 2008R2 DC versus XP SP3 on the same DC. However, I've got some Win7 stations that lack the $ at the end of the Display name or lack a display ...