If the computer you are renaming has multiple IP addresses (multihomed hosts), you will be given the option to rename all instances of the computer name, or just the currently selected instance.

Computer names can be 2-255 alphanumeric characters, composed of uppercase and lowercase letters, the numbers 0-9, the minus sign (-), and the underbar (_). The first character cannot be a minus or underbar, and the name must be a minimum of 2 characters. Dots can be used in the middle of a name when it is separator for a qualified domain; for example bigmachine.bigcompany.