Bill seems to think the answer depends on one's theory of reference, and in particular on a notion of 'successful (or otherwise) reference'. I'm not so sure.
This has been a large discussion ranging over multiple postings and indeed websites, so I may well have overlooked something. But all contributors so far seem to be using the phrase 'the same X' as if it were transparent and unproblematic. If only it were so. It seems to me that 'the same X' is ambiguous between what we might call a 'de re' sense and a 'de dicto' sense. If I say,
It looks identical but this is not the same car as the one involved in the accident,then I'm clearly using the de re sense. There are two distinct individuals in play. If I say,
He wasn't the same man after the accident,then I'm using the de dicto sense. There is just one individual in play but two distinct descriptions or conceptions of it.
Everyone agrees that the Christian, Jewish, and Muslim conceptions of God/Yahweh/Allah are divergent, so they cannot be the same, de dicto. Could they be the same in the de re sense? This seems to be where the concerns with reference come in. But I think the answer here is quite simple. If the founding scriptures of Christianity, Judaism, and Islam are true, then God, Yahweh, and Allah are different names for the one god. If, in particular, there is a unique creator of the world, called God by Christians, Yahweh by Jews, and Allah by Muslims, then these names refer to a single individual. This much seems inescapable. But these are big ifs.
And no theorising about reference in sight, to boot.