I believe that is more of a function in your MyVerizon account online. You would change something to share your caller ID, but I don't recall what steps there are.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
Log into your on-line 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 (if appropriate), then scroll down a bit and choose how you want your Caller ID to appear, then click Submit.