You can't let it go can you. For a start the people of the Byzantine empire themselves refered to themselves as Romans. The south of Italy was even part of the territory of the Byzantine empire -
https://en.wikipedia.org/wiki/Catepanate_of_Italy
Also Muslims did conquere Italy, they held Italian territory for 500 years. Where do you think all the dark haired Italians come from?
https://en.wikipedia.org/wiki/History_of_Islam_in_southern_Italy
You have a wonderful imagination regarding Spanish Islamic society. Many rulers of the Muslim world, wether Spanish or not engaged in non Islamic lifestyles, this did not translate through to alter the fundemental fabric of Islamic society.
Unfortuantely the same cannot be said for Christendom. You people have made a mockery of your own religion. It was torn into two by an English King who wanted to divorce his wife! Today you have homosexual marriages and preachers. I have no issues with someones sexuality, I am a liberal, as far as I'm concerned people are free to be openly gay, but even I draw the line at re-writing a religion to fit someones sexual whims.
Regarding the city - Istanbul, you might have known it as Constantinople. Better than ever!