No, it’s not named after the planet, nor the Disney dog. The “dwarf planet” Pluto was discovered by astronomers (1930) long after this waterfall in Watkins Glen State Park was named; in fact, the waterfall was named long before the park was created (1906).
Here’s how a guidebook from the 1870s described the twisted falls:
I think Pluto Falls was named for “the ruler of underworld in classical mythology”, which, perhaps, this narrow and dark section of the glen suggested to Morvalden Ells, who wrote the guidebook. The name is still used today.