Some may, it depends on when that book was written..
IIRC, some say Allah too.. It also means "The Lord".. in Arabic..
And some say Yahweh..
But Israelites turned away from using Baal as a word for the Hebrew God..
It became associated with a pagan religion in direct conflict with Judaism..
This happened well before Christianity, and an additional 600 years before Islam..
The Syraic religion was still prominent up to the Babylonian captivity, even among the Jews. Kings is full of it, with its moral theme being the question whether this or that ruler will side with the Yahwehists against the rest of the religious traditions around them, or not. Despite occcasional attacks on paganism it recurs. There is no uniform Yahwehist religion among the Jews until the return from the Babylonian captivity.
And that was due to the Persians first of all. They enabled the return and the rebuilding of the temple precisely to give homage to monotheism. The Persians were at that time moral monotheists, though by later standards of the dualist or Manichean stripe.
Every religious tradition in the ancient world was built on top of pagan predecessors. Islam fits that pattern, but it is a pattern and not an exception. The first external sources referring to Islam - Armenian histories about a century after its rise - refer to it as a version of the religion of Abraham. A revision, in other words, to a precursor of Judaism. That doesn't mean that is what it is, it just means that is how it was "sold" to the middle east, early on.
The actual operative cause of its rise, on the other hand, was the generalship of Omar, who exploited the rivalry between Persia and Byzantium to conquer the near east in record time. Islam can be viewed as a syncretic ideology meant to appeal to both camps while rejecting elements unacceptable to the other - with the camps in question being Byzantian Christianity and Persian Zorastrianism (its own moral monotheism, of Manichean stripe - and incidentally the historical source of the idea of a day of judgment, which was very prominent in early Islam).
There is no reason to go outside well known history to explain Islam.