Is it possible for a person to believe that Islam is God's message but remain a non-Muslim?

I find the way you express your question rather curious. There is present some contradiction in terms. If you are a believer in Islam, implementing it in your life, you are a believer. So how can you be a non-Muslim at the same time? Islam requires us to believe in God's oneness and in the Prophet Muhammad's message. If you declare that you believe in these, you are a Muslim. It is not sufficient to acknowledge this within yourself. You have to make the declaration, or the Kalimah, as it is often expressed in Islamic languages. This is expressed in Arabic as Ashhadu an la ilaha illa Allah, wa ashhadu anna Muhammad Rasool Allah. This means: "I bear witness that there is no deity other than God, and I bear witness that Muhammad is God's Messenger."

You seem to be troubled with the question of identity, particularly changing your name. I can tell you that this should be no trouble at all. You certainly can retain your name and be a Muslim. There is no such a thing as a Muslim name. When Prophet Muhammad, peace be upon him. preached his message and people became Muslims, he did not change their names except in a few cases. When we look at these, we find that all the names he changed were of three categories:

1) They represented beliefs that are contrary to the basic principles of Islam, as in the case of a name indicating belief in an idol;

2) The name had a bad meaning, as in the case of a person whose name meant "fire"; and

3) A name that indicated that the person had a high rank with God. In this last case, the Prophet, peace be upon him. told the person that he could not make such a claim, because judgment belongs to God.

Where a name reflected none of the above, new Muslims retained their names. The same applied to newcomers to Islam who belonged to other cultures. Therefore, people who adopt Islam today need not change their names in the same way as the Prophet's companions did not change their names on adopting Islam.