Your phone can be configured to reflect different CallerID per line appearance. It can also be set to "block" your CallerID. See example below using a 6 line appearance phone where line appearance 5 and 6 are set to block. If a user where to select that line appearance button and make a call the ID would not be revealed to the called party. (Note) this feature would need to be set by a system administrator.
Full detail can be found in the Star2Star Advanced System Configuration Guide for system administrators. (see page 12)