With regard to the use of "Allah" in Islam as the proper name of the god of Islam, I agree it's a different entity.
But please see my comment #17 above. "Allah" is not an incorrect name for our Christian God, since in many languages it is exactly analogous to us calling our deity "God" (rather than, say, "Yahweh"). It's just language usage, and the name "Allah" predates Islam by a thousand years. It's historically bogus for Islam to confiscate the term and force-apply it only to the god of Mohammed.
Gotcha. Thanks for the explanation.