Where did the New York giants get their name from?

Answer 1

The New York Giants got their name from New York's giant buildings.

Also, they wanted a name to boast to the other teams. So they picked "Giants".

The New York Giants also got their name from the Baseball team, the New York Giants, who later moved to San Francisco.

Answer 2

Between 1925-1957 there used to be two major league teams in New York called the Giants, one in the NFL and one in MLB. To keep from confusing the two, the term was used.

The MLB New York Giants moved to San Francisco for the 1958 season.