How is it that the Arabs knew the name Allah (such as the Prophet's (Sallallahu Alaihi wa Sallam) father's name before Islam came to introduce the name Allah through the Qur'an. I understand other religions such as Christianity had the name Allah but in this form since they were written in languages other than Arabic!

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

For sure, Arabs were believers in the existence of Allah before the advent of Islam, and they even used the same word "Allah". They believed that Allah is The Creator, The provider, The Only Owner of everything, The Administrator of life affairs and believed in other meanings of Divinity. But, they worshipped idols, according to their claim, to bring them nearer to Allah.
In this vein, Allah Says (interpretation of meaning): {And if you (O Muhammad SAW) ask them: "Who has created the heavens and the earth," they will certainly say: "Allâh." …} [31: 25]. He also Says: {Say (O Muhammad SAW): "Who provides for you from the sky and from the earth? Or who owns hearing and sight? And who brings out the living from the dead and brings out the dead from the living? And who disposes the affairs?" They will say: "Allâh." Say: "Will you not then be afraid of Allâh's Punishment (for setting up rivals in worship with Allâh)?"} [10: 31]. He also Says: {… And those who take Auliyâ' (protectors and helpers) besides Him (say): "We worship them only that they may bring us near to Allâh." …} [39: 3]. He also Says: {And they worship besides Allâh things that hurt them not, nor profit them, and they say: "These are our intercessors with Allâh." …} [10: 18].
Allah knows best.