Unfortunately, that doesn't work on the CDMA ViP. This is from the VZW website:
Originally Posted by medic0712
Caller ID Blocking
To Deactivate Caller ID on individual outbound calls:
Dial the number.
Press SEND. The words "Private," "Anonymous," or some other indicator will appear on the called party's Caller ID device instead of your wireless number.
To Deactivate Caller ID on all calls to a specific number:
Press *82 + the number + SEND.
To permanently block your number from being displayed on any phone:
Sign-in to My Verizon.
Click on the My Plan tab.
Click on Add/change features.
Check the box near "Caller ID Blocking."
Click the Next button at the bottom of the form.