As far as I understood it, yes, a black hole, or rather the event horizon around it, is perfectly round. The problem you describe is that you can’t see the black hole, as that is the whole point of why they are called black. What you can see though, is the light behind the home that gets blocked.

That gets an additional problem, since the gravity of the hole bends space time around it and you cana indeed see the part that is behind it, albeit distorted around the event horizon. What you describe as changing view from up or down is indeed just the different view behind the hole, not the hole itself.