Is it permissible to name Islam "Muhammad's religion" and Muslims "Muhammadans," based on the fact that the Prophet, may God's prayers and peace be upon him, is the one who brought Islam?

Islam has two meanings: a specific one and a general one. The specific Islam is the Shari'ah brought by Muhammad, peace be upon him. As for the general Islam, it is the religion of all prophets, based on the Oneness of God and following His messengers. The name "Islam" is the proper noun for this religion and its followers, "Muslims," and it is what God named them. As for calling Muslims "the Ummah of Muhammad" or "Muhammadiyyah," it is permissible in the context of clarifying the Imam of the Ummah, with the caveat that some enemies of Islam use this analogy to liken Muslims to Christians.