Alex functions as a short form of Alexander or Alexandra, inheriting the Greek sense of "defender" while shedding some of the longer name's formality. Its brevity and unisex use have made it read as adaptable -- a name that moves easily between contexts rather than announcing a fixed identity.
Make the Sun, or any of the superiors to signify princes and great persons. Scribes and rusticks, [are shown by] the inferior planets, and chiefly the Moon. - William Lilly (1602.-1681.)