Historically speaking it is true that there was a separate "Allah" mythology before Islam and a separate YHVH (or El, Elohim, etc.) mythology or even several before Judaism and Christianity. All three monotheistic religions have roots in elements which existed long before the pertaining scriptures. And insofar as these elements are separate it is correct to say the gods are not the same. However, that's not very useful because Islam is a reinterpretation of the old pagan faith in the terms of the surrounding monotheistic religions, just as Christianity is a reinterpretation of Judaism, and insofar they focus on the same divine being. Myths get reinterpreted and transferred from one protagonist to another all the time. In pre-scripture times that was how it was done. Different peoples met, and when they got along they began exchanging stories about their gods. And they translated those gods just like they translated language. For example, all accounts of the Great Flood agree that there is a main protagonist as the sole survivor (sole plus his family at least, but the important one is just the partriarch), and this person is called variously Atrahasis, Ziusudra, Utnapishtim and Noah, and the stories differ in almost all respect except the statement that this person built a vessel and survived the flood. Of course that's no god in either of the stories, but the same is true for all the various Els and Baals and whatnot.

And saying that "Allah" is purely Arabic and not Hebrew is about as useful as saying that "finger" is pure English and not German (which uses the same word for the same thing), forgetting that the common root for Allah and El and the other versions mentioned is a family of languages called Semitic. So the name is not a good argument for stating that different gods are referred to either.