Usually, when you are calling someone, your contact name shows up on the screen of the person who receives the call.
To call someone without showing your Caller ID, do following:
1) Open the Phone app and go to the Keypad/Dial menu
2) Type #31#
, followed by the phone number (Example: #31#016056934351
or #31#+4916056934351
).
3) Perform a casual call