Open Settings
Scroll down and tap Phone
Tap Show My Caller ID
Turn off Show My Caller ID
If Show My Caller ID is not available:
Contact your carrier
Ask them to block your caller ID for outgoing calls
To block your number for a single call:
Dial *67 before the phone number
Example: *67 555-123-4567
To unblock your number again:
Go back to Settings
Tap Phone
Turn Show My Caller ID back on