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The root of the name is uncertain, since no early forms have been found (in 1929 to 1931 Deer is used in Moore's History of Devonshire). A suggested back-formation is from Derriton, perhaps supported by aqua de Dyraton from 1282 in the Assize Rolls.
References
Eilert Ekwall (1928). English River Names. OUP. p. 118.