The plastic disc was invented in California, but its name comes from a pie bakery in Connecticut.
The disc itself belongs to Walter Frederick Morrison. Wikipedia says he and his future wife, Lucile, tossed a popcorn can lid after Thanksgiving dinner in 1937. Later, on a beach near Los Angeles, someone offered them 25 cents for the cake pan they were throwing. Morrison saw a market.
After the Second World War, Morrison and a partner, Warren Franscioni, began making plastic discs by 1948. They sold them as the "Flyin-Saucer," a nod to the UFO sightings then in the news. In 1955 Morrison designed a new model, the Pluto Platter. He sold the rights to the toy company Wham-O on January 23, 1957.
Wham-O's founders, Richard Knerr and Arthur "Spud" Melin, then heard that college students had their own word for the thing. They called it a "Frisbie."
That name came from a bakery. William Russell Frisbie founded the Frisbie Pie Company in Bridgeport, Connecticut, in 1871. Students at nearby colleges supposedly made a game of tossing its empty pie tins, according to Connecticut History.
Several colleges claim to have started the game. Wikipedia names Yale, and its article on the bakery credits students at Middlebury. Etymonline mentions Princeton as another claimant. Connecticut History calls the pie-tin story entertaining but unproven.
What is solid is Wham-O's choice. In June 1957 it gave the disc the brand name Frisbee. The spelling was changed from the bakery's "Frisbie," reportedly to avoid legal problems. Etymonline credits Morrison with that change. Etymonline says Wham-O registered Frisbee as a trademark in 1959.
The bakery did not live to see the craze. Wikipedia says the Bridgeport factory closed in 1958, while Connecticut History puts the closing in 1957.
The family name goes back much further. Etymonline traces Frisbie to Frisby, a place in Leicestershire. That place name means a farmstead or village of the Frisians. So the flying disc is named, through a pie company, after a North Sea people.
Frisbee is still a registered trademark of Wham-O. That is one reason organized sports played with the disc use the generic term "flying disc" instead.