Edit: OK, I think I see what you are referring to, the confirmation page that you can print directly from the web page. Agreed, it does not have Verizon's name on it, and it most definitely should. But at least it does have a confirmation number on it. Strange.....
I am leaving my original response below because one solution would be to ensure you request the confirmation email from Verizon, which most definitely does have their name on it. I print the confirmation from the web page to a PDF and save that, plus I request (and receive) the email confirming payment, and I save both indefinitely. And yes, I am paranoid....
Huh? I paid my bill online last week and here is the confirmation email I received ($ and account number deleted):
I see Verizon's name in multiple places. Maybe you are talking about some other kind of confirmation? If so can you provide details?
FiOS TV: Extreme HD, Internet: 50/25, Digital Voice
VMS Enhanced Service: 1 server, 2 clients
Keller, TX 76248 (VHO 1)