Are you talking about how it appears to others? If so, log into your MyVerizon account. Click on More Actions (in blue on left-hand side). Look under Device, and click on Share Name ID. At the top, choose which line needs to be changed, then scroll down a bit and choose how you want your Caller ID to appear, then click Submit.
I normally put 'on-line MyVerizon account' in the hopes that folks know to log in via a computer rather than phone, but I realized after seeing your note that I'd left 'on-line' out ... oops! Thanks for catching that!
Just to verify: You went to your on-line MyVerizon account, clicked on More Actions (in blue on the left-hand side under I Want To), and about half-way down under Device, you didn't see Share Name ID?