A 'workgroup' is simply a logical grouping of computers.  On a network, only a single workgroup is needed.  If all of your computers are not in the same workgroup, they may not be able to see each other correctly.  Just make one up and stick to it. Keep it simple and easy to remember.

Each computer should get the SAME WORKGROUP name and a DIFFERENT computer name. Again, keep all names simple and easy to remember.

Fun Network Naming Examples  Workgroup: Atom Computers: Neutrino, Quark, Electron, Proton, Neutron, etc... Workgroup: Sol Computers: Earth, Mars, Venus, Jupiter, Saturn, etc...  Workgroup: Milkeyway Computers: Sirus, Centauri, Vega, Deneb, Canopus, Proxima, Rigil, etc...

From your desktop, right click the "Network Neighborhood" or the "My Network Neighborhood" icon and select Properties.

You should see a screen that looks like the one below.

  

Type in the workgroup name you have selected and a unique computer name that is easy to remember.

You are finished with this computer.  Now you can:

or

From your desktop, right click the "My Computer" icon and select Properties.

You should see a screen that looks like the one below. 

  

Type in the workgroup name you have selected and a unique computer name that is easy to remember.

You are finished with this computer.  Now you can:

or

From the start menu, right click the "My Computer" icon and select Properties.

Select the "Computer Name" tab and you should see a screen that looks like the one below. 

  

Type in the workgroup name you have selected and a unique computer name that is easy to remember.

You are finished with this computer.  Now you can:

or