patronymic (n.)

"a name derived from that of parents or ancestors," 1610s, from Late Latin patronymicum, from neuter of patronymicus (adj.) "derived from a father's name," from Greek patrōnymos "named from the father," from patēr (genitive patros) "father" (see father (n.)) + onyma "name," Aeolic dialectal variant of onoma "name" (from PIE root *no-men- "name"). As an adjective, "derived from the name of a father or ancestor," from 1660s. Related: Patronymically.

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Definitions of patronymic from WordNet
patronymic (n.)
a family name derived from name of your father or a paternal ancestor (especially with an affix (such as -son in English or O'- in Irish) added to the name of your father or a paternal ancestor);
Synonyms: patronym
patronymic (adj.)
of or derived from a personal or family name;