nylon (n.)

polyethylene terephthalate used as a textile fabric, 1951, proprietary name coined by E.I. du Pont de Nemours & Co.; an invented word of no etymology, on the model of nylon, etc.

type of manufactured fiber, 1924, chosen by National Retail Dry Goods Association of America, probably from French rayon "beam of light, ray," from rai (see ray (n.1)) and so called because it is shiny. A marketer's alternative to the original patented name, artificial silk (1884) and the other marketing attempt, Glos, which was "killed by ridicule" [Draper's Record, June 14, 1924].

[T]he production of rayon in American plants, which in 1920 had been only eight million pounds, had by 1925 reached fifty-three million pounds. The flesh-colored stocking became as standard as the short skirt. ... No longer were silk stockings the mark of the rich; as the wife of a workingman with a total family income of $1,638 a year told the authors of Middletown, "No girl can wear cotton stockings to high school. Even in winter my children wear silk stockings with lisle or imitations underneath." [Frederick Lewis Allen, "Only Yesterday," 1931]

By coincidence, Old French rayon had been borrowed into Middle English centuries earlier as a name for a type of cloth.