Network name is the unique name that differentiate a MAC or PC on a network. If you have more than one MAC and you start sharing things back and forth between your computers, the names of those MACs start to matter.
On Mac OS X, changing computer name is extremely easy. How to change it? Just open up System Preferences, go to Sharing, and change the computer name. You may need to change the name under your Network setting also. Open Network (next to Sharing), Advanced, WINS, and change the NetBIOS name. Done!