Rugby

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mid 19th century: named after Rugby School (see Rugby), where the game was first played.

wiktionary

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1823: Named after Rugby School in Warwickshire, where William Webb Ellis "with a fine disregard for the rules of football as played in his time, first took the ball in his arms and ran with it, thus originating the distinctive feature of the rugby game". The place name Rugby is attested in the Domesday Book as Rocheberie, possibly equivalent to rook +‎ -by.

Borrowed from Cebuano rugby, from EnglishRugby, a brand of rubber cement by Bostik.

etymonline

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rugby (n.)

type of football, 1864, from Rugby, name of the public school where the game was played, which is named for its location in the city of Rugby in Warwickshire, central England. The place name is Rocheberie (1086), probably "fortified place of a man called *Hroca;" with second element from Old English burh (dative byrig), replaced by 13c. with Old Norse -by "village" due to the influence of Danish settlers. Otherwise it might be *Rockbury today. Or first element perhaps is Old English hroc "rook."

The Rugby Union was formed in 1871. Slang rugger for "rugby" is by 1893, with -er (1).