God

From OpinionJournal's Best of the Web:

Last week in Britain, a reporter asked President Bush if "Muslims worship the same Almighty" that he does. Bush replied: "I do say that freedom is the Almighty's gift to every person. I also condition it by saying freedom is not America's gift to the world. It's much greater than that, of course. And I believe we worship the same god." The Washington Post reports that the president's ecumenism prompted a kerfuffle among evangelical Christians:
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Bush is right. Christianity, Islam and Judaism are all monotheistic religions, united in the belief in a single God. (Muslims often call God by the Arab name Allah, but then so do Arabic-speaking Christians and Jews.) The three religions conceive of God differently, and Muslims and Jews do not share the Christian belief in the divinity of Jesus Christ. A Christian may well believe that Islam's conception of God is wrong, but if you believe in only one God, it makes no logical sense to describe a fellow monotheist as worshipping a "different" God.

Well, I wonder. Imagine the following argument:

A: "Aristotle died in 322 B.C."

B: "I thought he died in 422 B.C."

A: "No, in 422, he hadn't been born yet."

Clearly, both A and B are talking about the same Aristotle; it's just that they disagree on the contingent details of his life. But now imagine the following argument:

A: "Aristotle was an ancient Greek philosopher who died in 322 B.C."

B: "Look, I'll grant that Aristotle was a philosopher in his spare time, but he was neither ancient nor Greek. In fact, Aristotle was a Swedish-American television repairman from South Dakota who died last year at the age of 72. My father went to high school with him."

Does it still make sense to say that A and B are talking about the same Aristotle? Isn't there some point at which A and B disagree over so many details that they might as well be talking about two different people? And where is that point?

In more technical terms, I guess what I'm asking is whether "God" is a rigid designator (see Saul Kripke's Naming and Necessity), such that in all possible worlds the name "God" refers to the same being even if the contingent facts about him are different? Or is it inherent in the concept of God that there are no contingent facts about him, and therefore no other possible worlds?