If you have an HBO MAX account direct from HBO, Verizon has nothing to do with it. You can use the login on any HBO MAX capable device.
If you subscribe to the HBO premium channel through FiOS, the subscription includes access to HBO MAX. You can login to HBO MAX using your Verizon credentials.
Verizon set-top-boxes do not have an HBO MAX app. If you want to access HBO content through a set-top-box, you need to subscribe to HBO (the premium channel, not HBO MAX).
If you have a smart TV, streaming stick, computer, tablet or other device with an HBO MAX app, simply use your HBO MAX credentials.