Is it permissible to call a son named Muhammad by the name of his deceased father?

It is from the Sunnah to choose a good name, as the Prophet, peace and blessings be upon him, said: "Indeed, you will be called on the Day of Resurrection by your names and your fathers' names, so make your names good." There is no harm in changing a name to another good name if it is for a benefit and does not involve any شرعي (Shar'i - Islamically forbidden) constraint.