as a European knowing that in speeches of some muslim fanatics Spain is mentioned as Andalusia, which should be conquered (‘back’) - the name Cordoba also gives me the shivers. Its history does not mean much if crazy people use it as a symbol of muslim imperialism. If the mosque’s name was more neutral (Mecca mosque, al-Salam mosque, or so) and the financing was open and transparent, there would be less reason to complain.
Further, even though if Dialogue is what you would care about, setting up a whole islamic centre in the near of Ground Zero causing some 9/11 victims extra sorrow, is not - least to say - tactical and pretty insensitive. If I’d be in charge I’d go look for some other place. Dialogue is what I would want. Dialogue is what should be the main purpose. If dialogue is built on pain and sorrow in the hearts of those who lost their love ones, I would not want it anymore.

but that’s just my humble opinion