What is Patronymic?

Legal Definition
A patronym, or patronymic, is a component of a personal name based on the given name of one's father, grandfather (i.e., an avonymic), or an even earlier male ancestor. A component of a name based on the name of one's mother or a female ancestor is a matronymic. Each is a means of conveying lineage. In such instances, a person is usually referred to by their given name, rather than their patronymic.

Patronymics are still in use, including mandatory use, in many countries worldwide, although their use has largely been replaced by or transformed into patronymic surnames. Examples of such transformations include common English surnames such as Johnson (son of John).
-- Wikipedia
Legal Definition
A surname. See Name.
-- Ballentine's Law Dictionary