A dog is generally seen as a creature that pads along behind its owner, rarely leaving him for long. The verb 'dog' - as in ideas such as 'bad luck dogged him all his life' - suggests the very same idea...that there is, effectively, no lasting escape from it. 'Black' was, presumably the colour applied to it because of the normal associations of that colour with evil, death, misery etc. Thus, Churchill's 'Black Dog' was an evil presence - depression - that rarely left his consciousness.