When Negril was smaller, the Lighthouse Road (also called the West End Road and One Love Drive) started at the roundabout and went west only as far as Tigress Lane. So, the West End is called the West End because that the direction the road went from the roundabout. Also, the point between 3 Dives and the property just south of it is the western most spot on the island, so it is really as west as you can get.
