FWIW. I have been ordering my iPhones directly from Apple for years. In my case I have AT&T for my phone service, but it should work the same with Verizon. When I order a new replacement phone, I select the cellular provider at that time. The process then asks if I already have an account with that provider, and since I do, Apple takes care of contacting that provider to activate the phone with them with the same phone number.
When the phone arrives, it already has the SIM card installed and activated so it is ready to use. I did not have to contact AT&T for anything during this process.
In addition, my original 2-year contract with AT&T has lapsed. Since then, I am on a monthly plan with them. Regardless, there were no issues getting the new phone with both the same month-to-month service and with the same phone number. I believe, you can also request a new phone number during the ordering process.