This wikiHow teaches you how to turn off caller ID on your Android phone so that your phone number doesn't appear on other people's screens.
Steps

Step 1. Open your Android's settings
This is the gear symbol

that you find among your apps. You can also find these by pulling down the notification bar from the top of the screen.
Some mobile providers do not allow you to turn off your caller ID. Be sure to make a test phone call before relying on these settings

Step #2. Scroll down and tap on Call Settings
You will find this under the heading “Device”.

Step #3. Tap on Voice Call

Step #4. Tap on Additional Settings

Step 5. Tap on Caller ID
A pop-up window will appear.

Step 6. Tap on Hide Number
Your phone number is now hidden through caller ID when you call someone.