The "Flatiron District" has been known by that name since the mid 1980s. It had been previously known as the "Photo District," due to the large number of photographer's studios. Another part of the area was referred to as the "Toy District," for the large number of toy manufacturers and the American International Toy Fair that takes place there annually.
In the mid 80s when the area became more residential, real estate agents renamed it to give it more appeal.
I like the information I also found about it in the Global Architecture Encyclopedia. This information complements what we saw and heard in our tours.
"Not well known among those not from the area, or not into historic architecture, the Flatiron Building is a favorite of New Yorkers and admirers around the world. Perhaps because it symbolizes so much of how New Yorkers see themselves -- Defiant, bold, sophisticated, and interesting. With just enough embedded grime and soot to highlight its details. The Flatiron's most interesting feature is its shape -- a slender hull plowing up the streets of commerce as the bow off a great ocean liner plows through the waves of its domain. The apex of the building is just six feet wide, and expands into a limestone wedge adorned with Gothic and Renaissance details of Greek faces and terra cotta flowers.
The building has two claims to fame -- one architectural, the other cultural. Some consider the Flatiron Building to be New York City's first skyscraper. It certainly was one of the first buildings in the city to employ a steel frame to hold up its 285-foot tall facade, but not the first. Some felt its shape (like a flatiron) was less artistic and more dangerous. They thought it would fall over, and during construction the Flatiron Building was nicknamed "Burnham's Folly."
The building's cultural legacy is a little more interesting and has passed into the local social consciousness as a fable. It is said that the building created unusual eddies in the wind which would cause women's skirts to fly around as they walked on 23rd street. This attracted throngs of young men who gathered to view the barelegged spectacle. Police would try to disperse these knots of heavy-breathers by calling to them, "23 Skidoo." This phrase has passed out of common usage, but its descendant, the word "scram" remains in a back corner of the American lexicon." Glass Steel and Stone; Global Architecture Encyclopedia