If you look at the history of professional sports in the U.S., the “nicknames” originally were the names.
Professional sports were popularized in the U.S. by baseball leagues in tehlate 19th century. Early in that era, most competitions took place among clubs located in the same area. These clubs were originally founded by gentlemen’s clubs, so they had those kinds of names.
So, in Brooklyn the Atlantic Club would play against the Eckford Club. In Baltimore, the Lord Baltimore Club would play against the Maryland Club. In Washington, the National Club would play against the Olympic Club.
So some of the more successful clubs became popular:
Athletic Club
Atlantic Club
Centennial Club
Eckford Club
Elm City Club
Forest City Club
Kekionga Club
Mansfield Club
Mutual Club
National Club
Olympic Club
Resolute Club
Western Club
As the professional game became more popular, clubs started traveling to other cities to play against more distant rivals. It became customary to add a city name to specify where those clubs were coming from, especially since some club names were common in multiple places, and also, the “club” started to be omitted:
Athletic (Club) of Philadelphia
Atlantic (Club) of Brooklyn
Centennial (Club) of Philadelphia
Eckford (Club) of Brooklyn
Elm City (Club) of New Haven
Forest City (Club) of Cleveland
Forest City (Club) of Rockford
Kekionga (Club) of Fort Wayne
Mansfield (Club) of Middletown
Mutual (Club) of New York
National (Club) of Washington
Olympic (Club) of Washington
Resolute (Club) of Elizabeth
Western (Club) of Keokuk
At the same time, a trend was developing to refer to individual members of a club by the club name. So, a member of the Mutual Club was “a Mutual.” And when a group of them played, they were “the Mutuals.” So that trend was applied to teams generally:
Athletics of Philadelphia
Atlantics of Brooklyn
Centennials of Philadelphia
Eckfords of Brooklyn
Elm Citys of New Haven
Forest Citys of Cleveland
Forest Citys of Rockford
Kekiongas of Fort Wayne
Mansfields of Middletown
Mutuals of New York
Nationals of Washington
Olympics of Washington
Resolutes of Elizabeth
Westerns of Keokuk
Another trend was also in motion, however, and the geographic designation became more important, and newspapers started to reverse the names in tables:
Brooklyn Atlantics
Brooklyn Eckfords
Cleveland Forest Citys
Elizabeth Resolutes
Fort Wayne Kekiongas
Keokuk Westerns
New Haven Elm Citys
Philadelphia Athletics
Philadelphia Centennials
Rockford Forest Citys
Middletown Mansfields
New York Mutuals
Washington Nationals
Washington Olympics
In organized leagues, usually (but not always) the city name became so important that it was effectively the only official part of the club’s name.
Additionally, the success of the 1869-1870 Cincinnati Red Stockings solidified sock color as a popular way of identifying a club.
So the 1876 National League’s clubs were:
Athletic
Boston
Chicago
Cincinnati
Hartford
Louisville
Mutual
Saint Louis
By this point, the non-geographic part of the name was usually informal and impromptu. Sometimes there was a name that was widely accepted as the “real” name, sometimes not. Today, a lot of sources regularize the names of 19th century clubs using the modern format:
Boston Red Stockings/Red Caps
Chicago White Stockings
Cincinnati Red Stockings
Hartford Dark Blues
Louisville Grays/Colonels
New York Mutuals
Philadelphia Athletics
Saint Louis Brown Stockings
Even as late as 1901, however, there was no standardization. That’s why there’s no real agreement over what the “real name” of the American League’s Boston club was in 1901. It’s now officially the Boston Red Sox, but in 1901, it was really just “Boston.”
Over the first few decades of the 20th century, the two-part name, with a geographic designation first and a nickname second became customary, and club ownership stopped leaving the nickname up to popular agreement, designating it officially for marketing purposes.