Allah - "the one and only God in the religion of Islam. Etymologically, the name Allah is probably a contraction of the Arabic al-Il'h, 'the God.' The name's origin can be traced back to the earliest Semitic writings in which the word for 'god' was Il or El, the latter being an Old Testament synonym for Yahweh. Allah is the standard Arabic word for "God" and is also used by Arab Christians as well as by Muslims." - Encyclopedia Britannica.com.
The Britannica article above is OK except for its statement that El is an Old Testament synonym for Yahweh. El is sometimes used in Scripture as a title ('God') for YHWH (Yahweh/Jehovah). The usual title in Old Testament Scripture, also meaning 'God,' is Elohim. It is a common TITLE, whereas YHWH (Yahweh/Jehovah) is a proper name given by God Himself in Scripture. Allah has come to be used as a proper name, but it originated as a title, like EL, which simply means 'a god.'
So, yes, Allah is simply translated to English as 'the god.' Muslims, however, would probably tell us that it is a proper name for God.
For more, see:
"Some think that “Jehovah” in Hebrew means “Allah” (God). But..." (T-72 pp. 1-6, The Greatest Name; Watchtower Online Library)
The Greatest Name (JW.ORG)
ALLAH (Search Results From the Watchtower Online Library)