It is great to leave the skin on your vegetables when cooking so that you get the nutrients that are hiding just under the skin.  If you’re going for a chunky texture to this soup, then it’s fine to leave the skin on as long as you cut the potato into very small cubes so that you don't get a big mouthful of skin.  It will give a more earthy flavour but will still taste good.  However, for a velvety smooth soup, you will need to remove the skin, as the skin will affect the consistency of the soup and may make it bitty.