I realize that Allah is the Arabic name for the Judeo-Christian God and was used by Arab Christians and Jews before Islam, but I recently learned that Allah was also worshiped by pagan Arabs, along with his 'daughters' Uzzah, Allat and Manat. Another thing that always confused me was that that the name of Mohammad's father was Abdullah, 'Servant of Allah', even though he was presumably pagan.
Yes and no. Was there a deity being worshipped by that name in pre Islamic Arabia? Yes.
Among pagans it was a 'chief god', a 'leader of the Pantheon' type situation with other lesser idols being subordinate.
Is this the same God that was worshipped by Muslims after? Functionally, no. The fundamental premise of Islam is absolute monotheism. As it describes itself, Islam was born in reaction to these practices of associating other with God (shirk), practices it sees as cultural accessories that shroud the essential truth: that there is only one God. So even if the same name was being used, Islam fundamentally and categorically rejects the notion or role of God as a 'leader' of Gods or anything short of a singular and absolute authority. That's kindof the entire reason the religion had to exist in the first place, or so it claims.
So no, in actuality the same deity was not being worshipped after Islam arose, at least in its most basic premises and attributes. In regards to this deity having children, given that a major theme in Islam is the rejection of Christianity with the notion that "he is neither begotten nor begets", you can see how early Muslims would have viewed the prior pagan conceptions of Allah.
All that being said, what makes this more interesting is that the name was used by both Christians and Jews in reference to God as well, not just Arab Pagans. So I think it is put best in this line from my source:
Precedence indicates that each faith community has clearly defined its distinctive understanding of Allah through its contextual use, teaching and tradition.
That right there is probably the most succinct and best answer as to wether or not it's the same God that was being worshipped.
Excellent answers. More info: The early Muslims prayed facing Jerusalem (later changed to Mecca), and the Qur'an talks about most of the same prophets that are in the Torah and Old Testament, as well as Mary and Jesus. Since, in their view, there is only one god, it is the same god.
I worked with a lot of Arab Christians, and they (and the Muslims) thought they were worshiping the same god based on following different versions of the revealed message, like Jews versus Orthodox Christians versus Catholics versus Protestants versus Mormons versus Westboro Baptist.
Christian churches in the Middle East sometimes have the word "Allah" on the door, because it is their only word for (the only) god, just as English speakers use the English word 'god,' not the original Old Testament name.
Many Shi'a believe that when the judgement comes, the messenger will arrive at the head of a great host with Jesus at his right side.
Basically, each new iteration of the religion believes that they are following the clarified and corrected instructions, and that everyone else has failed to get with the program.