It is named after Elisha Kane, whose expedition in search of the lost Franklin expedition crossed it in 1854. Kane himself had named it "Peabody Bay," in honor of philanthropist George Peabody, the major funder of Kane's expedition.
^"KANE, ELISHA KENT". University of Toronto. Retrieved 2010-03-28. "A believer in the hypothesis of an open polar sea, he persuaded Grinnell, American financier George Peabody, the United States Navy Department, and several scientific societies to sponsor a second expedition to go north from Baffin Bay to the shores of the “Polar Sea” in search of Franklin. [...] The Advance then proceeded up the west coast of Greenland and into the sound Kane named Peabody Bay (later renamed Kane Basin) where, by the end of August, its northward progress was stopped by the ice."