Yes. In Hebrew the stem El- comes from the same proto-Semitic word which gave the Arabic Allah and Ellah in Aramaic. The term Allah was used by Palestinian Christians and Jews well before Islam came.
Similarly, Islam accepts that at the time of their original revelations, the Tawrah and Gospel of Jesus (which is not the same as the Gospels of today) were entirely valid revelations. Why would this be a teaching of Islam if the God of those books and scriptures was not the one of all three religions?
Allah was also used by Pagans it was there supreme-god (God of the lesser gods).
We belief that all prophets and messengers (peace be upon them) named god Allah(swt) we also further belief that Abraham and hes son Ishmael (peace be upon them) went to Arabia to build the Kaba where they taught people monotheism and the name ''Allah''. So when Mohammed(saws) came the name already existed.
We have something called Tahweed(One-ness of god) and it goes as following:
In the name Of Allah, The most Gracious, The Most Merciful.
Say, Allah is One,
Allah The Everlasting, The Eternal,
He has not given birth and was not born,
And no one is comparable to Him
Allah is the Light of the heavens and the earth
.. Light upon Light! And Allah guides to His Light whom He will.
Muslims acknowledge that Allah is the Creator, and He is the only One capable of giving life or taking it. All things are subject to Allahs Will. In the Quran, Allah tells us: "Allah created all things and He is the agent on which all things depend." (Az-Zumar 39:62); and, "Allah created you and whatever you do." (As-Saffat 37:96)
Understanding that Allah is the only Supreme Being means denying the existence of any other god. Allah has no partners, and the Qur'an rejects the concept of the trinity: "They do blaspheme who say, 'God is the third of three,' for there is no god except One God." (Al-Ma'idah 5:73)
Since Allah is the only God, only He is worthy of worship. In Islam, there is no such thing as an intercessor or intermediary. Each Muslim develops his or her own personal relationship with Allah by praying directly to Him and through other acts of worship such as giving to charity, reading the Holy Quran, and making hajj. Worship should be accompanied by full submission and obedience to Allah.
There are also 99 Attributes that can be found in the Islamic scriptures. Allah is unique in being called by these attributes. Allah states in the Quran: "There is nothing like Him." (Ash-Shura 42:11); and, "And never has there been anyone coequal with Him." (Al-Ikhlas 112:4).
The greatest sin in Islam is to engage in practices which contradict or compromise tawheed. This direct or indirect association of partners with Allah is referred to as shirk.
Shirk can take many forms. Praying to idols, praying to saints or prophets, practicing magic, fortune telling, believing in superstitions, and believing that amulets protect one from harm are all examples of actions which contradict the Oneness of Allah.
Associating is the same as believing that God's nature is three or that God is three or that there are three persons and these three persons are one god what logical speaking makes him three.