the event horizon is distorted from spherical

I suppose we use the term "spherical" in different ways. I mean it in the topological sense, to say "shaped like a ball, or a cube or a pear", as opposed to something with holes, like a donut. I guess you take it to mean "a perfect sphere", where it looks exactly the same from all directions (has spherical symmetry). In that sense, yes, there are just two kinds of stationary of black holes, the Schwarzschild one (non-rotating) and the Kerr one (rotating). There are no other kinds in 3D. However, in 4D there are also toroidal black holes, string-like and some irregularly shaped ones, too.