If you have the local IP address of a computer on your network, and need to get that computer's name, there is an easy method using the ping command in a Windows command prompt.
Open up a command prompt by typing "cmd" into the start menu search (Windows Vista, 7, or newer) or by opening a Run window and then running "cmd" (Windows XP).
Use the following command to ping the local IP address (change xxx.xxx.xxx.xxx to the IP address you want to ping):
ping -a xxx.xxx.xxx.xxx
The -a option of the ping command tells it to resolve the hostname of the IP address, so it will give you the name of the networked computer.
Full Network Discovery
If you need to get the hostnames and other information for all of the PCs on your network, I recommend using Advanced IP Scanner.