First: I've never heard of a Mormon named Muhammad, but nothing is impossible!! As for Muslims, no one has to name their first-born son Muhammad. BUT...a while ago my boyfriend and I were talking about something like this (he's from Morocco), and he said over in his country, it is VERY typical that the first-born son is named Mohammed/Muhammad, and the first-born daughter is named Fatima. Of course, he has an older brother and an older sister named Mohammed (they call him Maha at home) and Fatima. This practice probably goes on in other countries too. Last year I had a friend at school who was from Turkmenistan; his first-born son is named Resul and his daughter is named Maryam. One day I even asked him why he didn't name his son Muhammad. He said that his nephew is already named Muhammad. In his country, he said, after a man's death, the first grandson born would be named after his grandfather (if that makes any sense!). My friend's father was named Muhammad, and after this Muhammad died, my friend's brother named his next son Muhammad.
Second: This is what I have heard, and there is no evidence that would have me believe otherwise. Think of all the countries dominated by Muslim culture--from North Africa, Middle East, Central Asia, down to the Indian subcontinent. I can only imagine that most people from these lands have at least a cousin or uncle, if not a brother or father, named Muhammad or one of the variations of that name.