You know the rule: children inherit their father’s surname automatically in most countries of the world, with the notable exception, for instance, of Spain and South America, where both are given, but only the father’s passing on further.
For a long time, having your mother’s surname or a double-barreled one was considered out of the ordinary in Italy: the latter was a thing for the aristocracy, the former a sign that, perhaps, dad didn’t want to have anything to do with you, with good peace of women’s freedom of giving their own name to their child, if so they wished.