Islam is the only Monotheistic religion that condemned all types of idol-worship. It is not a new par se religion but a continuation and a completion of the previous monotheistic religions.
Muslims believe in One God Almighty, Allah. There is nothing in the history of Islam to indicate that an idol was named Allah, nor is there anything as regarding to the statement made in the question, but in actual fact, all idols that were kept in the Ka’aba was destroyed by Prophet Muhammad Peace Be Upon him, to the extend the pictures of previous prophets were also removed.
There is a reference to Prophet Abraham Peace Be Upon Him in the Qur’an in which he goes to a temple and destroys all the idols except one. He left this one Idol to prove his point that idols are helpless and thus he requested the idolaters to ask the one idol left for details as to what had happened.
The word ‘ilaah’ means god. This was referred to anyone/anything being is worshipped. The creed of islam is, ‘La Ilaha Illa-Allahu’ (“There is none worthy of worship except Allah).
I hope this answers the question