If you would like to call someone without your caller ID information being displayed, you can do so by dialing *67 before the phone number being dialed. As an example, this would call Mercury Network without displaying your caller ID information:
*678888664638
It is important to note that once you dial any number using *67, ALL of your outbound calls will stop showing caller ID information until you turn this feature back off. To do so, dial any phone number, but this time put *68 in front of the number. For example:
*688888664638
Now caller ID would be turned back on. Think of turning caller ID for your outbound calls on or off as a toggle, where putting *67 in front of any number toggles caller ID off for ALL of your calls, and putting *68 in front of any number toggles caller ID on for ALL of your calls.