Back in the early 1800's, a man named Chandler ran a trading post there, buying furs, deer hams and other items from settlers and sending wagon trains over to Buffalo Valley (now Johnson City, Tenn.). As immigrants moved on west, they asked Chandler to send their mail on out by wagon trains and they in turn used his wagons to deliver mail to those back home.
It was the custom of Mrs. Chandler to keep records of these messages in a large daybook. When folks would come into the store they'd ask if there was "anything for them in the daybook?" Naturally, when the government established an office there about 1815 everyone agreed that Daybook would be an appropriate name. The office was discontinued in 1957.