I came across an internet discussion where they were earnestly discussing whether 'God' and 'Allah' have the same reference. There are three positions that a Christian - who believes that the name 'God' has a reference, and that it refers to the supernatural and all-powerful being who is mentioned in both the Old and New Testament - could take on this.
1. 'Allah' is an empty name, referring to nothing. If you are a Christian description theorist, you believe that all propositions containing 'Allah' have an implicit existence claim, and so are all false. If you are a (direct) referentialist Christian, you hold that all such propositions are senseless, since they cannot have truth-value.
2. 'Allah' refers to a supernatural and powerful (though not all powerful) being who is not identical with God. Thus all the claims of Islam implying an identity with God, such as this passage where Allah speaks to Adam and Eve, are false. Others may be true.
3. God and Allah are identical, but Islam says many things about God that are not true. The only true things are the those relating to the Old Testament. For example, Allah expels Adam and Eve from Eden: God did do this, and Allah is identical with God, ergo etc.
What if 'God' and 'Allah' are both empty names? Can we make sense of such claims to identity or difference? I favour a 'haecceity predicate' theory of proper names. Being the very individual that you are cannot be a property of you. Otherwise, as Bill Vallicella has pointed out, all sorts of absurdities follow. How could the the 'thisness' of an individual exist even if the individual whose thisness it is does not exist?
But if proper names are not descriptions, haecceity is clearly a predicate, since we can make a predicate from any proper name thus: '-- is identical to Socrates' (or 'God' or 'Allah'). That is the only way we can make sense of narratives like the Koran and the Old Testament, which mention the same supernatural being as the same being throughout.