[2] The peak is situated in Glacier Bay National Park and Preserve at the entrance to Johns Hopkins Inlet, 100 mi (161 km) northwest of Juneau, and 5.6 mi (9 km) northeast of Mount Abbe, which is the nearest higher peak.

Although modest in elevation, relief is significant since the mountain rises up from tidewater in less than two miles.

Mount Cooper can be seen from Johns Hopkins Inlet which is a popular destination for cruise ships.

The mountain's name was proposed in the 1950s for William Skinner Cooper (1884-1978), a plant ecologist who performed vegetation-glacier relationship studies in the Glacier Bay area, and was chairman of the committee of scientists which proposed establishing Glacier Bay National Monument.

[2] The mountain's name was officially adopted in 1980 by the United States Geological Survey following Cooper's death.