For decades in the 19th century, the only major league team in Chicago was the Chicago White Stockings of the National League, who went on to become the Cubs.
When the American League planted a team in Chicago in 1900, they called themselves the White Stockings in homage to the former NL team. Later, the name was shortened to “White Sox.” So, the White Sox nickname is actually borrowed from the Cubs. Chew on that, South Siders. Strangely, the team has rarely worn white stockings.