Well, just because a character is described as being "Arabic" in a Hollywood theatrical movie, that doesn't mean that the screenwriters gave him an accurate Arabic name.
The movie character is "Ardeth Bay". The surname probably comes from the Turkish word "bey", meaning "chieftain", which was a title used by many leaders in the Muslim world and which often is written in English documents as if it was a surname.
I cannot find anything that looks like Ardeth in my Arabic name dictionaries. The closest names from the Middle East I have found are Ardad, listed as a Persian name meaning "deceiver" in Gandhi & Husain's The Complete Book of Muslim & Parsi Names, and Arda, listed as a male name meaning "king's staff" in my Turkish name dictionary. Perhaps the screenwriters consciously altered one of those, or perhaps they just made the name up.
Ardeth and Ardith are normally female names in the United States.