The Holiday Inn name began as a joke on a set of drawings. Kemmons Wilson's architect, Eddie Bluestein, borrowed the title of a Bing Crosby musical. Wikipedia says he meant it as a playful reference, and Wilson kept it.
The film came first. Holiday Inn premiered at the Paramount Theatre in New York on August 4, 1942. Bing Crosby and Fred Astaire starred, and Irving Berlin wrote the songs. Its hero, Jim Hardy, plans to turn a Connecticut farm into an inn that opens only on holidays. The film introduced "White Christmas," which won the 1943 Academy Award for Best Original Song.
The motel came out of a bad road trip. The Encyclopedia of Arkansas says that in August 1951 Wilson drove his family to Washington, D.C., in an Oldsmobile without air conditioning. The places they stayed varied in quality. Most charged extra for each of his five children. One room cost six dollars, plus two dollars a child.
Wilson, born in 1913 in Osceola, Arkansas, decided to build something better. The encyclopedia says his draftsman had watched the Crosby film the night before submitting the plans. It does not name the draftsman, while Wikipedia credits the architect Eddie Bluestein. Both agree that the film gave the chain its name.
The first one opened on August 1, 1952, at 4941 Summer Avenue in Memphis. That road was then the main highway to Nashville. It was called Holiday Inn Hotel Courts. The building was demolished in 1994.
The chain advertised itself with a roadside "Great Sign." Wikipedia calls it perhaps the company's most successful form of advertising. The original cost $13,000, and Wilson later called its replacement "the worst mistake they ever made."
The film title itself rests on an old word. Etymonline traces holiday to Old English haligdæg, "holy day," from halig, "holy," and dæg, "day." By the 14th century it could mean both a religious feast and a day off work. A word for a holy day became a Hollywood title, then a motel chain built for family vacations.