I wanted to put this in the How-To section, but did not know how to do so. I have noticed that most articles about how to hide your Caller ID or phone number from others when you make a call do not work with the Verizon Samsung Galaxy S4. The reason is they give the following instructions:
From the Homescreen go to Apps > Settings > My Device.
Open Call > Call Settings > Additional settings > Caller ID
Select "Hide number".
The problem is, with Verizon S4's there is no "Additional settings" under Call Settings.
However, there is a very simple solution to this problem. The following is what Verizon recommends and I find it works very well:
Blocking Caller ID when using your personal phone If you have to make a call on your personal phone but don't want just anyone to have your number, you can block Caller ID on your outgoing calls using Verizon Caller ID Blocking. Just press *67 before you dial your call, and "Private," "Anonymous" or "Restricted" will appear on the receiver's Caller ID readout. This service comes in handy for those who work in sensitive fields such as law enforcement. If you want to block Caller ID on all of your outgoing calls, you can set that up through My Verizon.
Keep in mind you cannot block Caller ID on your outgoing calls when you're calling 911 or toll-free numbers
I hope this is helpful. I had to do a lot of searching to find the solution to this problem. If there is a simpler solution, I would appreciate the input.