Singularity is a result of applying a theory of relativity in a case where we know relativity doesn't work, so it's unlikely it's real.
The event horizon is a three-dimensional null hypersurface, though, encompassing a four-dimensional spacetime "volume". You are probably referring to the two-dimensional apparent horizon, which depends on the spatial slicing.
Singularity is a result of applying a theory of relativity in a case where we know relativity doesn't work, so it's unlikely it's real.