This page contains historical maps from over five hundred years ago which clearly show the name Persian Gulf for the body of water between Persia and Arabia. 

Map of the World, Bologna edition of Ptolemy Geographia, 1482	Map of the World, Ptolemy Geographia. Venice: J.Pentius de Leucho, 1511	Map of Arabia, Munster,  Sebastian. Tabula Asiae IIII. Basel, Heinrich Petri, 1540.
Map of Arabia, Munster, Sebastian. Tabvla Asiae VI. Basle, 1542	Map of The Middle East by Sir Robert de Vaugondy in 1752	Map of Anatolia, from "A New Geographical and Historical Grammar" by Thomas Salmon, 1767
Map of Persia, by G. Long, M.A., 1831.	German map of the Middle East, by Landshut Vogel, 1842	Map of Persia, by John Tallis, 1851
	Map of Persia & Afghanistan, by S. Hall, 1854
Maps courtesy of the Persian Gulf Organisation