Ford paid for a huge search for a car name, then ignored the results.
In the mid-1950s the company was building a new mid-priced line, code-named the "E car." Ford asked its advertising agency, Foote, Cone & Belding, for names. Psychology Today says staff in the agency's Chicago, New York and London offices submitted 18,000, and about a third went to Ford. Wikipedia says the agency's report offered over 6,000. One executive, Ernest Breech, reportedly complained that the agency had been hired for one name, not 6,000.
Ford's market research director, David Wallace, had the names tested with the public. The favorites were Corsair, Citation, Pacer and Ranger. Wallace and his colleague Bob Young also invited the poet Marianne Moore to suggest names. Her offers included "Utopian Turtletop," "Mongoose Civique" and "Intelligent Bullet." Wikipedia stresses that her involvement was informal and never authorized.
The decision came at a meeting that Breech chaired while Henry Ford II was away. Breech rejected the four favorites and chose Edsel, after Henry Ford's only son. Edsel Ford had died in 1943.
His family did not like it. Henry Ford II, Edsel's son, reportedly said he "did not want his father's good name spinning around on thousands of hubcaps." Psychology Today says the family reluctantly went along.
The car launched on "E Day," 4 September 1957, as a 1958 model. It sold poorly. Wikipedia counts about 116,000 sales by November 1959, and Ford ended the program on 19 November 1959. Estimates of the loss run from $250 million to $350 million.
The researched names did not go to waste. Citation, Corsair, Pacer and Ranger all became Edsel model lines.
Etymonline dates the car name to 1956, the year the choice was made. It notes that "Edsel" came to mean "something useless and unwanted" almost as soon as the car appeared. It also traces Edsel as an English family name to the 14th century, linked to a place called High Edser in Surrey.