Does a name, especially if it carries the memory of a deceased person, affect a child's personality and destiny? And does it impose upon the mother the need to treat her son with excessive reverence that prevents her from disciplining him like other mothers?

It is permissible to name a child after the husband's father as a sign of respect and love, especially if the name is that of a prophet. The name does not prevent disciplining the child when they err. Indeed, the Prophet, peace and blessings be upon him, commanded disciplining children for prayer from the age of seven and striking them for it from the age of ten, and he did not exempt anyone. A name often has an influence on its bearer, but the hadith that prohibits striking or insulting someone named Muhammad is fabricated. The consideration lies in following the Prophet, peace and and blessings be upon him, not merely in his name.