I currently have HBO now on my Apple TV. That no longer comes up as a choice. How do I get HBO Max on my Apple TV?

Unless it isn’t available where you are, you should find it in the app store: https://support.apple.com/guide/tv/find-apps-atvb5a7dd799/tvos

It does require tvOS 12.2 or later

If you have an older Apple TV then it only runs pre-set channels via server. HBO removed their server version and created an app for HBO max. You would need to have an Apple TV HD (4th gen) or 4k (5th gen) in order to use it. The other option is to use airplay to stream from the app on iPhone/iPad.