Successful regional sales of the Pluto Platter soon caught the attention of the then new Wham-O, Inc., a maker of slingshots. After introduction, and a period of discussion and negotiation, Wham-O purchased the rights to the Pluto Platter on January 23, 1957, which happened to be Morrison's 37th birthday. 1957 was an interesting and fortuitous year for Wham-O: The Hula Hoop craze was catching fire, causing the company to temporarily divert materials and production effort to keeping up with the insatiable demand. But by the following year, the disc was back on track, and had been given the Frisbee name we all fondly recognize today.
The article also has a short history of the Frisbee.
To celebrate that occasion, even though I am a day late, here's a link to a nice treatment on the physics of Frisbees.