"Private" , "blocked" or Hide Caller Id Number (CLID)..

A few options:

Option 1 :  On the TN, CLS CLBA can block the number from being sent.

LD 20
Req       chg
type       Handset Type (Example : 1120,1210, etc)
TN        96 0 6 3
ECHG   yes

cls         CLBA
..


=============================================

Option B :  Create a Flexible Feature code for feature "CPP" - make the code *67

Dial *67+Acces Code+Phone Number
Example
*67914145551212


Use LD 57 - look for "CPP"

*67 is the standard US dialing string for privacy