The history of the name Brooklyn Dodgers thanks wikipedia:
"By 1890, New Yorkers (Brooklyn was a separate city until it became a borough in 1898) routinely called anyone from Brooklyn a "trolley dodger", due to the vast network of street car lines criss-crossing the borough as people dodged trains to cross the streets. When the second Washington Park burned down early in the 1891 season, the team moved to nearby Eastern Park, which was bordered on two sides by street car tracks. That's when the team was first called the Brooklyn Trolley Dodgers. That was soon shortened to Brooklyn Dodgers."