Try this:

1.Look around for a option under your phone's call settings menu called "Show/Hide My Number"
2. When you select it, it will most likely be set to "network default," which means that displaying Caller ID information would be dependent on your carrier's network setup for your mobile number. Change it to "hide number" to have the phone ignore the network setting and stop reporting your caller ID information.

If it does not work or the option is not available, begin your call with *67, if you're in North America.

You may also contact your mobile service provider to see if they can or will block your name from being displayed and showing your location or "Wireless Caller" instead. source

What do you mean by making your number private?