First of all, we’d like to state that Islam emphasizes that Muslims should have good names and give good names to their children. The Prophet (peace and blessings be upon him) is reported to have said, “You will be called on the Day of Resurrection by your names and the names of your fathers, so have good names.” (Reported by Abu Dawud).
It is Islamically correct to name a boy Nuh Muhammad or Muhammad Nuh. Both are Islamically correct.
It should be clear that Islam does not oblige Muslim people to choose specific names, for their children, whether boys or girls. It is rather up to people to choose the names for their children. However, the name should bear a good meaning and does not contradict the Islamic guidance in choosing names.
As for the meaning of the name Nuh, we do not know its exact meaning. However, since it is a prophet’s name it is undoubtedly a good name.