A matronymic is a personal name based on the name of one's mother, grandmother, or any female ancestor. It is the female equivalent of a patronymic. In patriarchal societies, matronymic surnames are far less common than patronyms. In the past, matronymic last names were often given to children of unwed mothers. Other times when a woman was especially well known or powerful, her descendants would adopt a matronym based on her name.
Filipinos take their mother's maiden name as their middle name (similarly to the Portuguese and Spanish practice). Some Vietnamese names also function this way, not as a "tradition" of sorts, but as a style or trend, in which the mother's maiden name is the middle name of the child.
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. 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 (Cymru)
Matronymics are accepted in the Netherlands but are generally written as given names on identity cards. 
Individuals in Spanish-speaking countries are given two surnames, usually the patronymic followed by the matronymic. For example, the 2012 president elect of Mexico is Enrique Peña Nieto, Peña being his patronymic and Nieto his matronymic. He may be addressed as Señor Peña or as Señor Peña Nieto. The surnames may be hyphenated: Peña-Nieto. (Referring to him as Señor Nieto would be incorrect.)
Portuguese names have a family name which is usally the matronymic followed by the patronymic. For example, José Manuel Durão Barroso, former prime minister of Portugal, Durão is the first and maternal family name and the second or paternal family name is Barroso.
Due to the diversity of family structures in the United States, a considerable variation of naming practices has emerged, despite the fact that traditional, patrilineal naming practices still constitute a majority. Part of the relatively new variation is due to second-wave feminism, which influenced many women to seek ways of preserving their natal names, family histories and individual identities as distinct from that of their partners’. Therefore, it has become more common and accepted for two parents to give their children two last names, either with or without a hyphen. Also, it is becoming more common to merge surnames to create an entirely new surname, or invent a new surname from whole cloth; these options have the advantage of allowing for one, shared nuclear family name. Additionally, it is common for women in professional fields to keep their maiden name once they get married, often without pronounced feminist influences. In these cases, children typically are given the father’s name.
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 names.
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.
- Bowman, William Dodgson. The Story of Surnames. London, George Routledge & Sons, Ltd., 1932. No ISBN.
- Levi della Vida, Giorgio; Ḥabīb, MuḥAmmad Ibn; Habib, Muhammad Ibn (1942). "Muḥammad Ibn Ḥabīb's "Matronymics of Poets"". Journal of the American Oriental Society (JSTOR: Journal of the American Oriental Society, Vol. 62, No. 3 (Sep., 1942), pp. 156-171) 62 (3): 156–171. doi:10.2307/594132. JSTOR 594132.
- 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. 407-414) 36 (6): 407–414. doi:10.1086/474406. JSTOR 3141456.