The word “Allah” predates Islam by about 3,000 years (do a search of “Allah” on http://www.antimullah.com and read a very in-depth article that was also translated into Farsi (Persian) about the origins.
Simplistically, Allah was the name of an idol (the biggest wooden one) in Medina and after destroying the rest, Mohammad adopted this one (the most popular in the region) and told everyone to worship Allah.
No “God” here unless you are an idolater.
Better handle on Islam as a religion?
The word for God in many Arabic languages is a variation on the word “allah” (at least that’s how it sounds to us). It’s used by everybody as a sort of generic word for God. Mad Mo was from a pagan tribe, so he probably first heard it in reference to the pagan gods of that tribe. And obviously, that name contrasted with any of the ways in which the Jews indicated God (in general, it probably contrasted with the Christian term, too, although Christian Arabs would use a word that sounded somewhat like “allah”).
In any case, it’s not a religion, but it sure was a stroke of genius on his part to call it one.