It is difficult to talk about the shape of the event horizon because the ordinary definition of a sphere is "surface where all points are equidistant from a given point" is already complex in a differentiable manifold, but even more so when the distance is infinite because of a singularity (or the point doesn't exist/isn't unique because of geodesic structure). So you switch to a definition of "surface of constant scalar curvature with the topology of a sphere", the topology being important to distinguish it from a plane and a hyperboloid.
From there, I haven't personally done or seen the calculations of the shape of the horizon for Kerr or merging black holes, but my intuition is that it would be indeed peanut shaped for a merger (there are likely some saddle points). The coordinate shape certainly is but you can choose coordinates so that a Schwarzschild black hole is a coordinate peanut so coordinates aren't very meaningful.