Here's how Caller ID works. Sprint, like all carriers, only sends your phone number to the other party. If you add Caller ID restriction on your account, they do not.
The name that shows up on the recipient's end is dependent on the receiving party's phone or carrier. When Sprint updates your Caller ID name, it just sends that information along with your number to all of the landline carriers. They then update a database with that information. Whenever your name shows up, their switches access the database and send the name along with the number. If the number is blocked, the receiving carrier will send the recipient a set "name" such as "Unknown", "Private", or "Restricted".
Unlike landline companies, cell phone companies only pass the number through. They do not maintain a names database. It is up to the recipient of the call to add the number to their contacts so that a name shows up on the phone along with the number on future calls.
It depends on which phone you have. If you have an Android or a Blackberry phone, you can download an application to block private numbers. I am not sure about the other types of phones or what (if any) apps you can get for them.