In ancient Rome, a gens (plural: gentes) was a family consisting of individuals who shared the same nomen [gentilicium] and who claimed descent from a common ancestor ... The gens was an important social structure at Rome and throughout Italia during the period of the Roman Republic. Much of individuals' social standing depended on the gens to which they belonged. Certain gentes were classified as patrician, others as plebeian; some had both patrician and plebeian branches [stirps; plural stirpes]. The importance of membership in a gens declined considerably in imperial times, although the [nomen] gentilicium continued to be used and defined the origins and dynasties of Roman emperors.
Origins
The oldest gentes were said to have originated before the foundation of Rome (traditionally 753 BC), and claimed descent from mythological personages as far back as the time of the Trojan War (traditionally ended 1184 BC). However, the establishment of the gens cannot long predate the adoption of hereditary surnames. The nomen gentilicium, or "gentile name", was its distinguishing feature, for a Roman citizen's nomen indicated his membership in a gens.
The nomen could be derived from any number of things, such as the name of an ancestor, a person's occupation, physical appearance, character, or town of origin. Because some of these things were fairly common, it was possible for unrelated families to bear the same nomen, and over time to become confused.
Persons could be adopted into a gens and acquire its nomen. A libertus, or "freedman", usually assumed the nomen (and sometimes also the praenomen) of the person who had manumitted him, and a naturalized citizen usually took the name of the patron who granted his citizenship. Freedmen and newly enfranchised citizens were not technically part of the gentes whose names they shared, but within a few generations it often became impossible to distinguish their descendants from the original members. In practice this meant that a gens could acquire new members and even new branches, either by design or by accident.
Stirpes
Different branches or stirpes of a gens were usually distinguished by their cognomina, additional surnames following the nomen, which could be either personal or hereditary. Some particularly large stirpes themselves became divided into multiple branches, distinguished by additional cognomina.
Praenomina
Most gentes regularly employed a limited number of personal names, or praenomina, the selection of which helped to distinguish members of one gens from another. Sometimes different branches of a gens would vary in their names of choice. The most conservative gentes would sometimes limit themselves to three or four praenomina, while others made regular use of six or seven ...
Patrician and plebeian gentes
Certain gentes were considered patrician, and others plebeian. According to tradition, the patricians were descended from the "city fathers", or patres; that is, the heads of the family at the time of its foundation by Romulus, the first King of Rome. Other noble families which came to Rome during the time of the kings were also admitted to the patriciate, including several who emigrated from Alba Longa after that city was destroyed by Tullus Hostilius. The last known instance of a gens being admitted to the patriciate prior to the 1st century BC was when the Claudii were added to the ranks of the patricians after coming to Rome in 504 BC, five years after the establishment of the Republic.
Numerous sources describe two classes amongst the patrician gentes, known as the gentes maiores, or major gentes, and the gentes minores, or minor gentes. No definite information has survived concerning which families were numbered amongst the gentes maiores, or even how many there were. However, they almost certainly included the Aemilii, Claudii, Cornelii, Fabii, Manlii, and Valerii. Nor is it certain whether this distinction was of any practical importance, although it has been suggested that the princeps senatus, or speaker of the Senate, was usually chosen from their number.
https://en.wikipedia.org/wiki/Gens
The gens Calpurnia was a plebeian family at ancient Rome, which first appears in history during the third century BC. The first of the gens to obtain the consulship was Gaius Calpurnius Piso in 180 BC, but from this time their consulships were very frequent, and the family of the Pisones became one of the most illustrious in the Roman state. Two important pieces of Republican legislation, the lex Calpurnia of 149 BC and lex Acilia Calpurnia of 67 BC were passed by members of the gens.
Origins
The Calpurnii claimed descent from Calpus, the son of Numa Pompilius, the second King of Rome, and accordingly the head of Numa is found on some of the coins of this gens.
Branches and cognomina
The family-names of the Calpurnii under the Republic were Bestia, Bibulus, Flamma, Lanarius, and Piso.
Piso was the name of the greatest family of the Calpurnia gens ...
Praenomina
The principal praenomina of the Calpurnii were Lucius, Gaius, Marcus, and Gnaeus.
Publius was not a regular name of the Calpurnia gens during the Republic, but was used by the Calpurnii Lanarii.
https://en.wikipedia.org/wiki/Calpurnia_gens
The gens Calpurina includes, among of course many others:
Calpurnii Pisones
Lucius Calpurnius L. f. L. n. Piso Caesoninus, consul in 58 BC, and father-in-law of Caesar
Calpurnia L. f. L. n., the last wife of Caesar
Gaius Calpurnius L. f. L. n. Piso Frugi, quaestor in 58 BC, married Tullia, the daughter of Cicero
Gnaeus Calpurnius Cn. f. C. n. Piso, a partisan of Pompeius, & subsequently of Brutus & Cassius; subsequently pardoned; made consul in 23 BC
Gnaeus Calpurnius Cn. f. Cn. n. Piso, consul in 7 BC, accused of murdering Germanicus
Lucius Calpurnius Cn. f. Cn. n. Piso 'augur', consul in 1 BC
Lucius Calpurnius Piso, accused of plotting against the life of Tiberius in AD 24
Marcus Calpurnius Cn. f. Cn. n. Piso, the younger son of Gnaeus Calpurnius, consul of 7 BC; accused with his father but pardoned by Tiberius
Gaius Calpurnius Piso, consul in AD 41 with the emperor Claudius, and the instigator of the conspiracy against Nero in AD 65
Lucius Calpurnius L. f. Cn. n. Piso, consul in AD 57 with the emperor Nero
Gaius Calpurnius Piso Crassus Frugi Licinianus, consul in AD 87.
Exiled to Tarentum for conspiring against the emperor Nerva; exiled again for conspiring against Trajan; murdered early in the reign of Hadrian
Lucius Calpurnius Piso Frugi Licinianus, named heir by the emperor Galba, and murdered on the orders of Otho in AD 69
Calpurnii Bibuli
Marcus Calpurnius C. f. Bibulus, consul in 59 BC; an opponent of Caesar, and a partisan of Pompeius during the Civil War
Calpurnia, the third wife of Pliny the Younger
Calpurnius Flaccus, a rhetorician in the time of Hadrian
Calpurnius Asprenas, appointed governor of Galatia and Pamphylia by the emperor Galba, induced the partisans of the false Nero to put the usurper to death
https://en.wikipedia.org/wiki/Calpurnia_gens#Members