There will always be distortion when doing that, but you can utilize the fact that you can only see a part of the Planet, b<y cutting a UV Sphere in half and the Unwrapping it:

You can find planet Textures online (for instance here: https://www.solarsystemscope.com/textures/ ) and use the default UV Map of a UV Sphere, that does a decent job, but has some distortion towards the poles (those planet textures already ‘compensate’ somewhat for that distortion):

The first method is best for abstract patterns like in your example.