The crossword got its name backward. Its inventor called it something else, and a printing slip renamed it within weeks.
The inventor was Arthur Wynne, born in Liverpool in 1871, whose father edited the Liverpool Mercury. Wynne was working in New York, putting together the "Fun" puzzle page of the Sunday New York World. On December 21, 1913, the paper carried his new grid.
It did not look like a modern crossword. Biography.com describes it as diamond-shaped with a hollow center. The letters F-U-N were already filled in at the top. Wynne called it a "Word-Cross Puzzle."
A few weeks later the name flipped. Wikipedia and Biography.com both attribute the change to a typesetting error that printed it as "Cross-Word." Nobody changed it back. The hyphen eventually dropped out, leaving "crossword puzzle." Etymonline dates the word to January 1914 and the short noun "crossword" to 1925.
Wynne did not invent the idea of interlocking words from nothing. Wikipedia says he built on earlier forms such as the word diamond. Biography.com adds that, by some accounts, he was inspired by a childhood game called Magic Square, a word square that reads the same across and down. What he added, according to the writer Adrienne Raphel, was crossed words printed directly on the page with blocked-out squares.
The puzzle stayed a newspaper oddity for about a decade. Then, in 1924, the new publishing house Simon & Schuster issued The Crossword Puzzle Book in its first year. It became a bestseller. The New York Times held out much longer, treating crosswords as a passing fad. It started its own puzzle only in February 1942.
The name itself is plain English. Etymonline says the "intersecting" sense of cross dates to about 1600. Word goes back to Old English. Put them together in the right order, with help from a typesetter, and a Sunday filler had the name it still carries.