Etymology
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rayon (n.)

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.

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nylon (n.)

1938, coined, according to DuPont, from a random generic syllable nyl- + -on, a common ending in fiber names (compare rayon and later Dacron), said to be ultimately from cotton. "Consumer Reports" in 1939 called it "duPont's much-publicised new miracle yarn, which is scheduled to appear in 5,000,000 stockings next year and which is meantime giving rise to many rumors, hopes and fears." As an adjective from 1939. Nylons for "nylon stockings" is from 1940.

Nylon is the generic name chosen by the Dupont Company for a group of materials classed as synthetic linear superpolymers. It has also been defined as a "Man made protein-like chemical product (polyamide) which may be formed into fibers, bristles, sheets, and other forms, characterized when drawn by extreme toughness, elasticity, and strength." ["The Michigan Technic," August 1945]
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