Pool is what it sounds like. The liver bit being the mythical bird makes a sort of sense when you think how real birds get their common names e.g.oyster catcher,herring gull etc. Liver is a kind of seaweed. Eat breakfast in Wales, just over the border, and you'll find that there 'laverbread' is a variety of seaweed cooked mixed with oatmeal and eaten with bacon, sausages etc. One thing is sure; the waters of Lliverpool would have had plenty of seaweed. The mythical bird is portrayed as like a cormorant and often shown with seaweed in its beak.As a symbol it makes sense and so does its name, if it's associated with local seaweed.. The creature does not seem to exist in myth otherwise than as the symbol of the city.