Updating my fictional MLB uniforms and logos

Here's the origin per Wikipedia:

The early entry of this team in 1883 was simply the New Yorks, also sometimes called the Gothams, "Gotham" being a synonym for New York City. According to legend, manager Jim Mutrie was bragging to newspaper reporters about the stature of his players, "My big fellows! My giants!" and by about 1885 the name was stuck on the team for good.
"The club was first called the Giants about 1885. P.J. Donohue, New York World baseball writer, probably picked up a chance to get into a type argument with Harry Palmer] of Chicago and Charles F. Mathison of Detroit. All three scribes followed teams that had big men, were proud of that fact, and stressed the poundage and height of their athletes. The New York Nationals, after playing an exhibition game with Newark in 1886, were called Giants; and when they appeared in St. Louis later the same year, Joe Pritchard, Mound City expert at that time, alluded to them as the Gotham Giants." (BBG)
Although the "Giants" nickname was well established by 1900, the prosaic "NEW YORK" or simple block letters "NY" were used on uniform shirts until 1918 when "GIANTS" first appeared. (Okkonen)
Eventually the alternate nickname "Jints" (rhymes with "pints") was picked up as a colloquial pronunciation of the team name. It followed them, along with their real nickname "Giants", when they moved to the west coast in 1958.
The New York Giants of the NFL were named for the baseball team which was once their landlord.