The Qurash (aka: Quraish) tribe which Muhammad belonged to was in charge of idol worship at the Ka'ba Shrine.  The chief god of Muhammad's tribe was one of the three sister goddesses called al-Uzza, the youngest of the three daughters of the pre-Islamic Allah and the patron goddess of Mecca.  Her name means "the mighty one".  The other two were named "al-Lat and "al-Manat".  It was only by chance that a fortune teller counseled Muhammad's grandfather against sacrificing Muhammad's father to this al-Uzza pagan diety.  The head of these pagan deities was "Al-llah".  It is believed that "al-llah" in Muhammad's time before Islam referred to a vague moon god and that Muhammad believed that al-Uzza was a daughter of this "al-llah".  

The Qurash tribe's Allah corresponded to the god Bel, which is another name of the Assyrio-Babylonian gods En-lil and Marduk. It has the same meaning as Baal.  The Arabic today translates the word Allah as "God".  Muhammad's father's name was "Abd-Allah" (or slave of Allah).   When Muhammad says there is only one god - Allah - now you have an idea what his background/ thinking was.