But it wasn't until today, when I saw this article about the real Mae West, that it occured to me why the troops named the preservers after her. The Smithsonian site explains:
Mae West was a veteran of vaudeville and Broadway. She made her first movie and immediately became a national sex symbol when she was nearly 40. With her hourglass figure, saucy double-entendres, and sinful saunter on five-inch heels, she was a natural bombshell. During World War II, Allied soldiers called their inflatable life jackets 'Mae West' in honor of West's famously buxom figure.
(And here I am so confused. I thought hippies invented sex in the 1960s.)