One of the cheapest doubts of the enemies of Islam ever.

By merely spreading this kind of doubt, they have proven nothing but THEIR ignorance of history and Islamic beliefs. It is absolutely true that the PAGANS of Makkah used to call the one God by his unique name ALLAH, yet, this was not due to them having invented that name, rather it was the LEFTOVER of their FORMER MONOTHEISTIC heritage. The Arabs used to be MONOTHEISTS, they are the sons of Ibrahim, just like many other people and tribes the devil lured them into polytheism thus they had started to mix their MONOTHEISTIC faith and practices with polytheism. That is why Tawaf (around the Ka’bah) was still done under the pagans, yet, they had DISTORTED it by including polytheistic prayers to this practice which has a monotheistic ROOT as it was done by PROPHET IBRAHIM (AS) the FATHER of the Arabs. The Messenger of Allah (SAWS) did NOT came to destroy all customs of his people and the Christians and Jews, rather he came to approve the right and disprove the wrong, and no doubt, the Arab pagans who called God Allah, were upon the truth regarding that, since even the Christian arabs back then AND today call the one God ALLAH!

• (41:37) And  of His Signs are the night and the day, and the sun and the moon. 
• Do not prostrate yourselves before the sun, nor before the moon, but prostrate yourselves
• before Allah Who created them, if it is Him that you serve.

The star and crescent motif appears on a Gokturk coin of the second Turkic Kaghanate, from the first half of the 8th century AD found at Chach (Tashkent oasis). This suggests that the symbol was in use among the Turks (or at least known to them from Sogdian examples) prior to their arrival in Anatolia.
The crescent moon and star were mistakenly attributed to the Islamic faith. However, Islam has historically had no symbol or symbols – in fact there is a disdain within Islam for the use of iconic symbols – and many Muslims find its use blasphemous, even to this day. After all, the moon and star used in conjunction were originally pagan icons. Though the Crescent Moon and a Star appear on the flags of several Muslim countries, it should be seen more as a historical symbol of the land, the territory or the empire, rather than of a state religion. It was adopted by reformists who changed the Islamic Constitution.