A black hole has a spin, and spins about an axis which means that you can define a direction that it is pointing fairly straightforwardly

Black holes also aren't point like objects, the interior/singularity is completely divorced from the exterior of the black hole - they are a property of spacetime itself, not an effect that arises from the singularity

Astrophysical black holes formed from stellar collapse also don't have a singularity as viewed from an external observer