The stuff falling onto the black hole has an orientation -- it forms an accretion disk at the "equator".

If the black hole is spinning, it has poles. We expect all black holes to be spinning. This is a subtle change in the shadow itself, but...

And if the accretion disk and black hole have misaligned poles, there should be a huge warp in the disk close to the black hole as the black hole frame-drags the accretion disk.