Mohammedan is an archaic term in English for a Muslim that was commonly used in western literature until around the mid-twentieth century. Earlier generations of westerners falsely believed that the followers of Islam worshipped Muhammad, when actually Muslims worship only God (or Allah); Muhammad is regarded as the last prophet. The term is offensive to many Muslims, because of the word's implication that Muhammad is worshipped.I doubt that this is correct. I can't find any proof that westerners thought that anyone worshipped Muhammad. Eg, this 1910 encyclopedia does not say so.
The word only suggests that a Mohammedan is a follower of Mohammad, and that is correct. There are Mohammedans who prefer other terms, such as moslim or muslim, but I think that is for other reasons. The term Mohammedan is accurate.
Muhammad taught many things, besides religion. I think that the terms moslem, muslim, and Islam were invented for just the religious aspects of his teachings. The term Mohammedan is more correct if one wants to include his other teachings. That is why I continue to use it.