On a Mac: choose Apple menu -> System Preferences -> click Sharing, and at the top of Sharing preferences, under the computer's name, you'll see your computer's local hostname.
On a Windows computer: Start -> (All) Programs -> Accessories -> Command prompt. In the new pop-up window, enter "ipconfig /all", press Enter, and you will see the hostname of the machine, less the domain at the top, under the section Windows IP Configuration.