//it isn't just Mohammad, they disapprove of showing any living beings.//
That doesn’t apply throughout the Islamic world. In North Africa, for example, you’ll often find items decorated with pictures of people and animals, and portrayals of Mohammed by Muslim artists do exist.
http://tarekfatah.com/images-of-prophet-muhammad-from-islamic-art-and-history-before-the-clan-of-ibn-saud-took-islam-hostage/
The ban on art of that nature, along with the disapproval of music and dancing, emanating from the stricter versions of Islam, seems to be a more recent thing.
Boys are often named Mohammed in reverence to the Prophet.