Right click My Computer and select properties or open Control panel then System and the go to the computer name tab. Click the Change button.
Don't know if you have used XP before but MS got the help section nearly right this time. Give it a try next time you need some info like this.
This is from the help section with a search of "change computer name"
To rename a computer
You must be logged on as an administrator or a member of the Administrators group in order to complete this procedure. If your computer is connected to a network, network policy settings may also prevent you from completing this procedure.
If the computer is a member of a domain, you will be prompted to provide a user name and user password to rename the computer in the domain.