Isla de la Gente Barbuda = Santa Cruz Island

From Islapedia

Isla de la Gente Barbuda [Sp., island of the bearded people], the name given to Santa Cruz Island in 1602 by Sebastian Vizcaino. He had heard rumors that bearded men, possibly mariners from Europe or the Orient who had been marooned there by shipwreck, had been seen by the Indians.