What you are apparently unaware of is that by the time of Mohammad Jews had ceased using YHWH out of respect for the divine name and used other names like Adonai (Lord) and Elohim.
Delitzsch's etymology of Allah is hotly contested by Semitists like Lambdin, Muraoka and others. The Catholic Encyclopedia, while it is an extremely well-researched work, was published more than 80 years ago. Some of the most groundbreaking work in Semitic studies has taken place since WWII, including the discovery of entirely new Semitic languages and grammars like those of the Nabataeans and Ugarits.
The name El was the name of many local gods in the Middle East, it's true. But many of these gods had compound names in which El was a prefix meaning divinity. Which divinity was "El-Lah"? It's certainly not a name of God used by the Jews.
As others have pointed out, allah is and was the common noun in Arabic for god. Capitalized as Allah, it is a direct translation of our word God. What difference does it make that a term formerly used to refer to a pagan god is now applied to God? The terms used in the NT for God were titles or common nouns used to refer to the pagan gods. Does that mean that the NT somehow was not referring to the One True God?
Similarly, Mohammed makes very plain that when he uses the term Allah he means the One True God Creator of the Universe. I happen to not agree with his claim to inspiration by this God, but he certainly was not referring to any other.