I’m going to continue calling it the Cordoba House project, because that’s what its proponents are calling it - and what its own website continues calling it, when they aren’t referring to it as Park51. The group backing the project is the Cordoba Initiative, but one thing it most certainly isn’t is a Ground Zero mosque, since it is not located at Ground Zero.
It’s near Ground Zero, but so are strip clubs, bars, boutiques, hotels, residences, shopping centers, and office space. In fact, office space is one of the main parts of the rebuilding at Ground Zero - millions of square feet of office space. Oh, and hundreds of thousands of square feet of retail space too.