I don’t know about the Mud Hens. I’m sure every team has a history behind their nickname.
I can think of a few off the top of my head :
Chicago Bears were named after the Chicago Cubs.
Green Bay Packers were sponsored by a meat packing company originally.
Pittsburgh Steelers is in honor of the history of when Pittsburgh was a big steel producing city.
Buffalo Bills are named after Buffalo Bill Cody.
Detroit Lions was inspired by Detroit Tigers, both big felines.
Minnesota Twins are named after the twin cities they are located in.
Milwaukee Brewers are named after the historic status of Milwaukee as a major beer brewing city.
Colorado Rockies named after the Rocky Mountains.
Arizona Diamondbacks named after the snakes in the desert of Arizona.
“Chicago Bears were named after the Chicago Cubs.”
“After” - only in a ‘time’ sense.
Halas named them Bears because he wanted to be bigger.