This franchise originally (years ago) was the Southside Syndicate, a tribute to a great game (Syndicate Wars) and the city's traditional reputation as the Hitmen or ties to the mob. But, that was kind of played out with me, so I was looking to do something specific about the state, and I didn't want to use the state bird (Cardinals, because I'm a cardinal fan, and it was already used by the old Chicago Cardinals football team), so I came across whitetail deers, IL's state mammal or some such crap. As soon as I thought of the name Whitetails, it was obvious to use Chicago's nickname of the "Windy City" to get Windy City Whitetails. The very 1st OOTP universe I played (21?), I used the Windy City Whitetails.
The color scheme is from the flag of Chicago/police.