Scrabble is the game's third name, and by far the oldest word.
The game began with Alfred Mosher Butts, an architect who was out of work during the Great Depression. He first called his invention Lexiko. He then renamed it Criss Cross Words, the form given by the Scrabble Association and Dictionary.com. Milton Bradley turned it down in 1933, according to Dictionary.com.
The rescue came from James Brunot, an entrepreneur who bought the manufacturing rights and agreed to pay Butts a royalty, according to Wikipedia. Wikipedia and Dictionary.com both say Brunot renamed the game Scrabble. The Scrabble Association credits the two men together, saying Brunot worked with Butts and they came up with the name. The trademark was registered in 1948.
The word was not invented. Etymonline dates the verb scrabble to the 1530s, meaning to scrawl or make random marks. It comes from the Dutch schrabbelen, a frequentative of schrabben, "to scratch," which traces back to a Proto-Indo-European root meaning "to cut."
The meaning moved around. By about 1600 it also meant to scrape or paw with hands or claws. By the 1630s it meant to struggle or scramble, perhaps influenced by that second word. The noun for a confused struggle appeared in 1794, and a scrawled letter in writing in 1842.
The Scrabble Association describes the word as meaning "to grope frantically." Etymonline dates the board game's name to 1949, while the Association says the trademark was registered in 1948, a small mismatch between sources.
Business followed the name. In 1952 Brunot licensed Selchow & Righter to make the game, and in 1972 that company bought the Scrabble trademark, according to Wikipedia.