Is it permissible to add the mother's name alongside the father's name when registering a newborn, given that the newborn's full name in their home country follows their father's name?

There is no religious impediment to writing the mother's name in official documents, such as "Mother's name: So-and-so, daughter of So-and-so." What is forbidden is to attribute the newborn to his mother instead of his father, due to the severe warning against anyone who attributes himself to other than his father, as the Prophet, peace and blessings be upon him, said: "There is no man who claims to be the son of someone other than his father – while knowing it – except that he has disbelieved. And whoever claims to belong to a people among whom he has no lineage, let him take his seat in the Fire."