'rugby' (the name of the sport) originates from the English town 'Rugby', specifically from Rugby School in Warwickshire where a form of the game developed in the early 19th century.

'rugby' (the place name) was recorded in older forms in medieval English records and later became the modern place-name 'Rugby'; the sport took its name from the school in that town and then the word extended to mean the game and the ball.

Initially the word referred to the place (and the school there); over time it came to mean the school game developed there, and then more generally the sport and its ball.