How to Disable the Caller ID on an iPhoneby Tyson Cliffton
Apple enables the caller ID feature on the iPhone by default. While this feature is enabled, your phone number will appear on the display of phones you call that show a caller's number. When you disable caller ID on your iPhone, the text "Private" displays on the screen of phones you call instead of your phone number. You can disable caller ID through your iPhone's Settings menu.
Tap "Settings" on the iPhone's home screen.
Tap "Show My Caller ID" in the Calls section.
Tap the "ON/OFF" toggle next to Show My Caller ID until "OFF" appears. Your phone number now appears as Private.