Sometimes there are specific nicknames for a team's fans. Fans of the Green Bay Packers professional football (American) team are called "cheeseheads," because the state of Wisconsin, where the city of Green Bay is located, is known for making cheese. Fans of the Miami (Florida) Dophins professional football team are known as "dolfans," a pun on the word "fan" and the team name. However, the name of the team and the nickname of its fans are different, and fans of most teams do not have a nickname.
(Last night I watched the evening television news. The national professional football championship game, the Super Bowl, will be in four days. Our local team, the New England Patriots, will be in that game, so there was a lot of coverage in the program. The announcers said things like "There are a lot of Patriot fans here in Atlanta, but not so many Rams fans." This is typical.)