The story
Like many things used by impoverished people during the Great Depression (e.g. Hoover hogs, Hoovervilles), the dress was named after Herbert Hoover, US president when the Depression began, + -ette. (It has also been suggested that the name might not refer to the inexpensiveness but liken the dress's effectiveness as work clothing to Hoover's pre-presidential career as an effective administrator of aid to Europe after the First World War.)
Etymology from Wiktionary, CC BY-SA 4.0.