A matronymic is a personal name based on the given name of one's mother, grandmother, or any female ancestor. It is the female equivalent of a patronymic. Around the world, matronymic surnames are far less common than patronymic surnames. In some cultures in the past, matronymic last names were often given to children of unwed mothers. Or if a woman was especially well known or powerful, her descendants might adopt a matronym based on her name.
Terminology in English
The word matronymic is first attested in English in 1794 and originates in the Greek μήτηρ mētēr "mother" (GEN μητρός mētros whence the combining form μητρo- mētro-), ὄνυμα onyma, a variant form of ὄνομα onoma "name", and the suffix -ικός -ikos, which was originally used to form adjectives with the sense "pertaining to" (thus "pertaining to the mother's name"). The Greek word μητρωνυμικός mētrōnymikos was then borrowed into Latin in a partially Latinised form (Greek mētēr, dialectally mātēr, corresponds to Latin mater), as matronomicus. These words were a source for coining the English matronymic as the female counterpart to patronymic (first attested in English in 1612). Whereas the Oxford English Dictionary records an English noun patronym in free variation with the noun patronymic, it does not, however, record a corresponding noun matronym.
More rarely, English speakers use forms based wholly on Greek: the noun metronym (first attested in 1904); and the noun and adjective metronymic (first attested in 1868). These are, for example, the forms used in the 2016 The Oxford Dictionary of Family Names in Britain and Ireland.
The matrilineal communities in South and North-East India, like the Bunts and Khasi, have family names which are inherited from their mother. Matronymic names are common in Kerala. Daughters take the names of their mothers as the second part of their name.
Filipino names legally have the maiden name of the child's mother as a middle name as opposed to Anglo-American use of secondary or tertiary given names. Filipino children born to unwed mothers, if not claimed by the father nor adopted by anyone else, automatically bear their mother's maiden name and sometimes middle name.
Some Vietnamese names also function this way, as less of a "tradition" than a style or trend, in which the mother's maiden name is the child's middle name.
Although many English matronyms were given to children of unwed mothers, it was not unusual for children of married women to also use a matronymic surname. For instance, it was traditional during the Middle Ages for children whose fathers died before their births to use a matronym, and it was not unheard of for children to be given a matronym if the father's name was foreign, difficult to pronounce, or had an unfortunate meaning. A child of a strong-minded woman might also take a matronym, as might a child whose name would otherwise be confused with that of a cousin or neighbour. There are even instances where royal houses used matronymics to strengthen claims to the English throne – for example, Princess Matilda's eldest son was known as Henry FitzEmpress (-fitz meaning "son of" from Latin filius). Common English matronyms include Beaton, Custer, Tiffany, Parnell, Hilliard, Marriott, Ibbetson, Babbs, and Megson.
In the old Finnish system, women were standardly given matronyms, while men were given patronyms, for example, Ainontytär (female) or Pekanpoika (male). Since the 19th century the system of inherited family names has been used, however, and today nearly all Finns have inherited surnames.
Family names derived from matronyms are found in France, especially in Normandy: Catherine, Marie, Jeanne, Adeline. In medieval Normandy (Duchy of Normandy), a matronym might be used when the mother was of greater prominence than the father or the basis for a claim of inheritance, such as in the cases of Henry FitzEmpress and Robert FitzWimarc.
Ireland and Wales
Matronymics are accepted in the Netherlands but are generally written as given names on identity cards.
Family names derived from matronyms are also found in Russia. Examples include: Katin, Mashkov, Annushkin. Oleg Yaroslavich, 12th century prince of Galich, was known as Oleg Nastasyich during his life to distinguish his claim from that of his half-brother Vladimir.
An example of an Arabic matronymic is the name of Jesus in the Qur'an, ‘Īsá ibn Maryam, which means Jesus the son of Mary. The book Kitāb man nusiba ilá ummihi min al-shu‘arā’ (The book of poets who are named with the lineage of their mothers) by the 9th-century author Muḥammad ibn Ḥabīb is a study of the matronymics of Arabic poets. There exist other examples of matronymics in historical Arabic. 
Most characters in the Bible are referred to with a patronymic. However, Abishai, Joab, and Asahel – the sons of Zeruiah, sister or stepsister of King David – are invariably referred to as "Sons of Zeruiah" and the name of their father remains unknown. Also the Biblical Judge Shamgar is referred to with the matronymic "Son of Anat".
There are indications of a Jewish history of matronymic names. Specifically, in East European Jewish society, there appeared various matronymic family names such as Rivlin (from Rivka/Rebecca), Sorkin (from Sarah), Zeitlin (from Zeitl), Rochlin (from Rachel), Feiglin (from Feige), and others. In certain Jewish prayers and blessings, matronyms are used, e.g., "Joseph ben (son of) Miriam".
- μήτηρ. Liddell, Henry George; Scott, Robert; A Greek–English Lexicon at the Perseus Project.
- ὄνομα in Liddell and Scott.
- μητρωνυμικός in Liddell and Scott
- mater. Charlton T. Lewis and Charles Short. A Latin Dictionary on Perseus Project.
- "matronymic, n. and adj.". OED Online, 3rd edition. March 2018. Oxford University Press.
- "metronymic, n. and adj."; "metronym, n.". OED Online, 3rd edn. March 2018. Oxford University Press.
- The Oxford Dictionary of Family Names in Britain and Ireland, ed. by Patrick Hanks, Richard Coates, Peter McClure (Oxford: Oxford University Press, 2016).
- Mother's name becoming common in naming conventions in Kerala (page 201), shodhganga.inflibnet.ac.in; accessed May 18, 2017.
- Bowman, William Dodgson. The Story of Surnames. London, George Routledge & Sons, Ltd., 1932. No ISBN.
- Review, Iceland (5 March 2008). "In the Name of the Father". Retrieved 18 May 2017.
- Instituut, Meertens. "NVB : voornaam eindigt op 'zoon'". www.meertens.knaw.nl. Retrieved 18 May 2017.
- Levi della Vida, Giorgio; Ḥabīb, MuḥAmmad Ibn; Habib, Muhammad Ibn (1942). "Muḥammad Ibn Ḥabīb's "Matronymics of Poets"". Journal of the American Oriental Society. Journal of the American Oriental Society, Vol. 62, No. 3 (September 1942), pp. 156-71. 62 (3): 156–71. doi:10.2307/594132. JSTOR 594132.
- Miku, Linda M. "Brickbat's - May 2006 LoP Page". atensubmissions.nexiliscom.com. Retrieved 18 May 2017.
- Cross, Earle Bennett (1910). "Traces of the Matronymic Family in the Hebrew Social Organization". The Biblical World. JSTOR: The Biblical World, Vol. 36, No. 6 (Dec., 1910 ), pp. 407-14. 36 (6): 407–14. doi:10.1086/474406. JSTOR 3141456.