The term "Mohammedan" was only used in the Christian West, never by Muslims themselves. And the reason is strong, the reason is that both Judaism and Islam absolutely refuse to worship men. Only Christianity does this by turning Jesus into a god.
Each religion is named after what is their core. The core of Christianity is Christ. The core of Mormonism is The Book of Mormon. The core of Islam is submission to God as described in the Quran. ("Islam" means submission.) The core of Judaism is the Jewish race. I think the core of our religion is the Old Testament which is why I like Mikra-based names. In Hebrew, Mikra is basically mi-kara where "mi" means "from" and "kara" means "to read" or "what is read". The word Mikra is the old Hebrew word for the Old Testament.
https://en.wikipedia.org/wiki/Mikra