The basin at the top of the canyon was great for grazing and had been deeded to Samuel Snyder, Heber C. Kimball and Jedediah Grant. The settler's name it Parley's Park City. Over the year's the Parley was dropped in the name, Park City became the town's official name.
However, the name of Heber C. Kimball is still all over the area. i.e. Heber City, Heber Ave and Kimball Junction. The Canyons ski area is actually in Snyderville (Samuel Snyder) not Park City. But since Park City is the desired destination of millions of tourist, the name Snyderville is rarely used and businesses and residents use Park City as their address.