Is it obligatory to name the child "Muhammad" in order to be blessed by the Prophet, peace and blessings be upon him, knowing that the visionary saw the Prophet in a dream and kissed his hands, and wishes to name her newborn "Zayd"?

It is not obligatory to name a child Muhammad because of a dream or otherwise. The matter of names is broad, as long as there is no prohibition concerning it. There is no impediment to naming him Zayd. Seeing the Prophet, peace and blessings be upon him, in a dream is true, and Satan cannot impersonate him if his description matches the characteristics mentioned in the Sunnah.