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The correct question would be "why is it called Arabian Nights". The answer is that this was a decision by the English translators, and has little to do with the original work. As explained in the second sentence of the wikipedia article you linked to.
Suppose someone would decide to translate the Song of Roland into English and give it the title "The Song of the French". Should we then ask why the work is mostly set in Spain?
One thing to keep in mind re. Persians is that the Abbasid court in Baghdad was located only a few dozen kilometers from where the (Persian) Sasanian court had been located earlier (and before that the Parthian and, for some time, the Seleucid court), in Ctesiphon. A story set in Baghdad, but several hundred years earlier, would automatically have been set in the Sasanian capital.