 Galveston Island was originally inhabited by members of the Karankawa and Akokisa tribes who called the island Auia . The Spanish explorer Cabeza de Vaca and his crew were shipwrecked on the island or nearby in November 1528 , calling it " Isla de Malhado " ( " Isle of Bad Fate " ) . They began their years @-@ long trek to a Spanish settlement in Mexico City . During his charting of the Gulf Coast in 1785 , the Spanish explorer José de Evia named the island Gálvez @-@ town or Gálveztown in honor of Bernardo de Gálvez y Madrid , Count of Gálvez . 
