The Wilkes Expedition, in 1841, named the island after John Shaw, a United States Naval Officer. According to Bill Tsilixw James, hereditary chief of the Lummi Nation, the Lummi know the island as Sq'emenen. A San Juan Island resident proposed to the state Board of Geographic Names in 2015 that Squaw Bay be renamed Sq'emenen Bay; that proposal generated a compromise proposal from the Shaw Island Historical Society to rename the bay Reef Net Bay, in recognition of the reef net fishing historically and currently done there. The name "Reef Net Bay" was adopted.