From what I've gathered, in the Muslim & Islamic faiths' Bible (Quran), Jesus prophesied the coming of the prophet Muhammad who was basically to be the one who covers the rest of the word of god.
Allah is God in Arabic, it's not the name of God, it's just different like:
Dia is God in Gaelic Scottish, Diyos is God in Filipino, Dumnezeu is God in Romanian, etc etc.
So honestly when you think about it, Islamic, Muslim, Christianity, Catholicism, and other off-shoots are for the same God, just different messengers.