Yes, and it is still common practice in Iceland. For instance their prime minister is Steingrímur Hermannsson ("Hermann's son"), who is the son of Hermann Jónasson ("Jónas' son"). Icelandic doesn't even know "family names".

Similarily, Russian knows the patronymic form as a middle name: Putin's full name is Vladimir Vladimirovich Putin ([o]-vich denoting "son of") and could be addressed, even semi-formally, as "Vladimir Vladimirovich".

The purpose would be the same as a family name's: to identify a person by his or her descent. In smaller societies, a proper family name is not necessary.

"Houses" are mostly used for royal or ruling families and denotes noble descent, i.e. that a family is part of the ruling class in a feudal society.