For Muslims, God is unique and without equal. They attempt to think and talk about God without either making Him into a thing or a projection of the human self. The Koran avoids this by constantly shifting pronouns to discourage believers from inadvertently reifying God and creating any physical image of Him.
God is known in Arabic as Allah to distinguish Him from ilah, which could refer to any of the gods once worshiped in Arabia. Just as one might say in English that the French or Germans worship God, not Dieu or Gott, so one should properly say that Muslims worship God, not Allah, which is simply the word for God (with a capital G) in the Arabic language. Giving a different name to the one God worshipped by the followers of Muhammad erroneously implies that their God is different from the one God worshipped by Jews or Christians.