The name obviously has multiple layers:
To honour the Firemen/women who have served--hence the chest stripe that has been on the jersey since day one--the alternate logo used to be a Fire truck, as well as the current logo being similar to that worn by the CFD.
To honour our city's history--not so much revere the fire that destroyed our flegdling city, but the means by which the 'second city' was built and those who made the foundations for what we, that live here/are from here, consider to be the greatest city on Earth.
To show fire, the raw passion, grit, determination that this city and it's residents are known for--the shoulders that carry the heavy load and put the work in to get the job done.
The club may not win everything all the time, but it has known success in its short history, and has shown every bit a part of the Chicago culture as any other team--except mass acceptance of it's standing in the sports pantheon. That will come with time and as long as the Chicago Fire remain true to form and true to the city. At least every opponent that comes here to play knows that they will not have a walkover and that we will give them a hell of a game.
That is part of why the name fits. I hope others see that too.
