That generally would be on the user's side AFAIK. Or, you can contact your service provider and see if they have the option to display your name and number. I know that most of the major carriers allows you to do so like Verizon and AT&T as well I believe.
This is a long time feature so it should be on any version of iphone unless you do not have caller id provided by Verizon. And I thought it was a part of Verizon's iphone service so maybe you can check again in Settings.
Verizon will add the toggle for "Show Caller ID" for $2.99 per month. My ID shows all the time. But if I don't want it to show, I dial *67 then the number. That's easier than going to settings and turning the toggle, which I'm not going to pay for.