They wont have domain names. If you are running a server, they will be a member of a domain.
If you have a workgroup then each computer will have a unique name. to find out the name of a particular computer, click on "Start", right click on "My Computer", click on "Properties", and then click on the "Computer Name Tab."
This will show you the name of the computer and the name of the workgroup (network).
Hope this helps.
-Rob