Is it obligatory to name a male newborn Muhammad, due to the supplicant's saying in his supplication: "O Allah, if You have created a creature in my wife's womb, then make him male so that I may name him Muhammad, for the sake of the owner of this noble and honored name, our master Muhammad, may Allah's peace and blessings be upon him"?

You are not required to name your male child Muhammad, because what you said is not a vow. And your statement in the supplication, "by the right of the owner of this name," is not permissible, for seeking intercession through the status of the Prophet, peace be upon him, is not permissible according to the preponderant opinion, because it has no effect on the attainment of the desired outcome, and it is not a sound means for supplication.