I have been listening to a podcast, called "The History of Byzantium" and in one of the episodes there was a discussion about the lack of reference to Mohammad or Qur'an in the century after his death, and Muslims were referred as Ishmailets, Saracens, etc. but never any reference to the prophet. It sounded like the Caliphate from Damascus somehow created an image of Mohammad. After that period, an Islam that is more similar to our days' version emerges, with references to its prophet, and the holy text.
I haven't been able to find any sources on this discussion, what I have been able to find is a link to this book, which I haven't read yet; http://www.amazon.com/Did-Muhammad-Exist-Inquiry-Obscure/dp/161017061X
Can someone give a modern historic outlook of beginnings of Islam, and the existence of its prophet? Also please correct if there are any mistakes in this text.