A black hole itself (the singularity) is 1 dimensional - a single infinitesimal point. The event horizon around it is roughly a sphere. The diagrams that you are talking about are a visual metaphor that represent 3D space as a 2D plane and the 3rd dimension standing in for the influence of gravity. IRL, spacetime has 3 spatial dimensions, not 2, and gravity is not a dimension but a force. It's hard to visually represent gravitational distortion of 3 dimensional space without a 4th spatial dimension to do it with, so textbook diagrams use a 2D plane.