settings,phone,show my caller ID,ON
That is whether or not to send the NUMBER on on outgoing call.
The OP is asking that Verizon populate the names of the subscribers in the caller ID databases. Evidently, Verizon isn't doing that.
Personally, I don't care. Most friends have a cell phone, which never handles names via caller ID (cell phones look up the number in address book). Anyone with caller ID at home recognizes my number, or some have the name. But it's a personal preference, could see it either way.
AT&T used to have "Wireless caller" or some friends would see "Calif. Wireless" or something similar. Now it has my name. Either way, I usually call people I know, or businesses that would have my name anyway, or would need it!