Personally I think it's a bit of a shame that this new venture - essentially in the railway arches to the north - has taken the name of the square itself (ie the public open space / highway) and turned it into a brand.
It kind of takes something away from the other businesses and activities in the square that aren't part of the new thing.
In the 1920's my mother used to walk from her home in Snowsfields to her work ( hard labour) for a fruit and nut company on the Southbank as it is now known. Her route covered the full length of Union Street and involved crossing Flat Iron Square. I always thought it was known by that name by the locals and was not a proper street name. I also used to think that the term 'The Obelisk' was a local term for St. Georges Circus but have since discovered that 'The Obelisk' was the proper term.
It was an island, in the shape of an iron, yes triangular. Took me ages to forget that was a public lav, cheers Chelsea ;) I like the look of that café though, always reminds me of being abroad and I could go in and buy a li-lo and some goggles.