Named after Spanish naval officer Juan Francisco de la Bodega y Quadra (1744-94). According to Raincoast Place Names, in 1792 Quadra "sailed to Nootka Sound to meet Captain George Vancouver and, as Spanish commissioner to the Nootka Sound Convention, arrange British access to the Pacific Northwest and restore confiscated British property. He and Vancouver were not able to come to terms but established a firm friendship and agreed to give the name Quadra and Vancouver's Island to the large body of land that Vancouver had just circumnavigated. It was only later that this name was shortened to Vancouver Island. Quadra, unwell, returned to Monterey and died not long after at Mexico City."
Quadra Island, Francisco Point and Bodega Anchorage on Quadra Island are also named after Juan Francisco de la Bodega y Quadra.