I just tried watching part of The Eagle on HBO GO and it played just like it should and looked great. No cut off heads or anything else.
A few days ago I watched an episode of Strike Back on MAX GO and it played great as well. I never thought I'd enjoy watching movies or TV episodes on a small phone screen, but it wasn't hard to watch at all and I was very impressed with the quality.
I don't know if your resolution is off because of a problem with your phone, or the HBO GO site. I didn't see any place to adjust the resolution settings, but I think that your video quality is automatically adjusted for your device.
It probably doesn't matter where you start first, but I'd probably start with the cable provider and if they can't help, try Verizon.
Sorry I couldn't be more help.