As muslims believe Allah is the Lord from the beginning before time itself and will remain the same.
We also believe Him to be the Lord who sent the Prophets, Noah,Moses,Jesus etc, hence my guess would be that the word "Allah" is not a new one, but this word must have been common among many, and maybe some people used the name for their own beliefs.
Does not mean that when muslims use it they are referring to the moon.
As I am no expert....
Here;s what Wikipedia says
Allah - Wikipedia, the free encyclopedia
Allah (Arabic: اﷲ, Allāh) is the standard Arabic word for "God", derived from al-ilah, the God.[1][2] The term is best known in the West for its use by Muslims as a reference to God.[3] Arabic-speakers of all faiths, including Christians and Jews, use the word "Allah" to mean "God".[4] The Muslim and Christian Arabs of today have no other word for 'God' than 'Allah'.[5] In pre-Islamic Arabia, Allah was used by pagan Meccans as a reference to the creator-god, possibly the supreme deity.[6]
In Islam, Allah is the only deity, transcendent creator of the universe, and the judge of humankind.[3][1] Some Islamic scholars believe that the term "Allāh" should not be translated, arguing that "Allāh" as used in Islam is a special and glorified term whose use should be preserved, while God can also be used in reference to deities worshiped by polytheists.
According to F. E. Peters, "The Qur'an insists, Muslims believe, and historians affirm that Muhammad and his followers worship the same God as the Jews.[Qur'an 29:46] The Quran's Allah is the same Creator God who covenanted with Abraham". Peters states that the Qur'an portrays Allah as both more powerful and more remote than Yahweh, and as a universal deity, unlike Yahweh who closely follows Israelites.[7]
According to the tradition of Islam there are more than 99 Names of God (al-asma al-husna lit. meaning: "The best names") each of which evoke a distinct characteristic of Allah. The most famous and most frequent of these names are "the Merciful" (al-rahman) and "the Compassionate" (al-rahim).[8][3]
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also the following from the same article
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Translation
Some Muslim scholars feel that "Allāh" should not be translated, because they perceive the Arabic word to express the uniqueness of "Allāh" more accurately than the word "god" for two reasons:
The word "god" can take a plural form "gods", whereas the word "Allāh" in their view has no plural form.
The word "god" can have gender as male god or female god (called goddess) whereas the word "Allāh" in their view does not have gender.[15]
This is a significant issue in translation of the Qur'an.
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:)