This isn't about etymology. It's irrelevant how God and Allah were derived. What's relevant is how they're used today.
You will find as much consistency in the Islamic world as in the Christian or Jewish worlds. If you look at the Monotheistic Abrahamic faiths, it is the Christian sects that, by and large, are the most deviated from the Old Testament norms; in particular as far as the Trinity goes. The Jewish and Muslim view of God is far closer to a pure monotheism.
Louis in German is Louis, obviously.
It's Ludwig, not Louis. Both names have their origins in Old Franconian; in which the name was Chlodowig. They are equivalent, but with various pronunciation changes over the last 1500 or so years. You see, a funny thing happens to words, they evolve in pronunciation and in meaning.
But the word "allah" is merely the Arabic word for "god", and etymologically is related to similar words in other Semitic languages, including the Hebrew "el". If you're an Arabic Christian, you will use the word "allah" for the same reason. For goodness sakes, mate, the Aramaic word for God is "elah".