The story
The city in Alabama, originally Woodstock, was renamed by town officials in 1873 (after realizing there was another village named Woodstock in central Alabama) in honor of Annie Eliza Scott Tyler (1838–1914), daughter-in-law of Daniel Tyler, one of the two organizers of the Woodstock Iron Company, which started the then planned community. Equivalent to Annie + -s- + -ton (“Annie’s town”). The name of the city in Missouri was changed in 1894—a transfer from the city in Alabama.
Etymology from Wiktionary, CC BY-SA 4.0.