Allah اللّهُ originally means "The God". Like in English and many other languages, the Arabic word is inherited from a wording that has been used for pagan deities, إِلَه ,ilah, which was an unspecific term for all deities; the deities were given proper names to distinguish them. Allah has also become a proper name, as it is not spoken al-ilah "the god" but ligated. I have read that the main god in the polytheist Arabic belief was also called Allah. The Arabic Christians already said Allah.
As we do no more believe in deities, it is no more necessary to have a proper name for The Only God. Instead, we have 99 attributive Names for One God.
Hebrew has several names for The God, too, which the Jews do not pronounce any more for fear to misuse it:
YHWH, Elohīm, and the answer God gave when Mose asked for his name, אֶהְיֶה אֲשֶׁר אֶהְיֶה, that may be translated to «I Will Be Who I Will Be» or «I Am Who I Am» - rather a refusal of a given name.
Using Allah to name Him in English puts the stress on the Arabic source of our belief. Using God (written always with capital G) to name Him puts the stress on the belief that there is no god but The God, and we do not believe in a deity different from the God of our Jewish and Christian brothers.