Why do these Hubble images of Neptune look like Cheela?
Neptune has an axial tilt of 28.3 degrees and an orbital period of 164.8 Earth years; currently, the north pole is tilted away from Earth.
The maps in your question were each constructed from twelve exposures of Neptune: four each in 845 (red), 547 (green), and 467 nm (blue) wavelengths.  Each of the exposures was then converted from an effectively-orthographic view of a hemisphere of Neptune to the equirectangular projection used in the maps.  The precise technique is cited to https://iopscience.iop.org/article/10.3847/1538-3881/aaa6d6 and https://iopscience.iop.org/article/10.1088/0004-637X/812/1/55.
The bumpy appearance comes from using four discrete observations rather than a single continuous one; the black area is portions of Neptune that were never visible.  Each of those spikes is the result of projecting a single color of a single pixel on the edge of Neptune's visible disk onto an equirectangular map.