The Roman Republic and its foundation
The earliest period of Rome was the monarchy but is filled with problems. The sources for it were written hundreds of years later and thus our accounts do not agree with each other - or archaeological evidence. In contrast our sources for Greece at this time are much more abundant. Livy's first book (ab urbe condita) is the earliest account but from 500 years after the period he was writing about. Despite this problem, it does provide context and opinions of how Romans viewed their origins.
Roman Naming Convention
A freeborn male Roman of an aristocratic family typically had three names:
• praenomen – a first name used by family and friends. By the Republican period only 18 names were current from an earlier pool of 40ish names, many of which had fallen into disuse. They could be shortened into an initial (e.g. M = Marcus, Mn = Manlius, G = Gaius).
• nomen – a family name, like modern usage.
• cognomen – a nickname specific to branches of a larger family (e.g. Scipio Africanus vs. Scipio Nasica)
e.g. Gaius Iulius Caesar (anglicized into Gaius Julius Caesar)
Our modern naming contention is entirely haphazard. So Titus Lucretius Carus is called by his nomen Lucretius while Quintus Horatius Flaccus is anglicized into Horace but Marcus Tullius Cicero is called by his nomen (and referred as ‘Tully’ in the romantic period). For women, they took their father's nomen (e.g. Julius Caesar's daughter is named Julia) and differentiated by numbers (prima, secunda, tertia...) or maior/minor.
Titus Livius (cognomen unknown)
He was born in Padua in 59 BCE and died 17 CE in Rome. Somehow he became known to Augustus and at age 30, he devoted himself to writing ab urbe condita, from the earliest history to his current period. We've only got some of his 142 books but some summaries remain covering the lost material. They moved diachronic, tracing the history of Rome through the ages in an annalistic fashion (history by year).
His story starts with the Aeneas’ flight from Troy and ended in book 142 with the death of Drusus in 9 CE. His narrative style is interesting for a historian and reads like a drama, a very different conception of history than modern works. The ancients called his style "milky rich". Livy had a huge nostalgia for the Roman past, that their ancestors were infinitely more virtuous and thus more "Roman" - incorruptible, honourable, and incredibly frugal. Citizen-soldiers who always did the right thing - or so they were envisioned. They were obsessed with following the mos maiorum (“customs of the ancestors”) which created an incredibly conservative society. To Livy the present was troubled and contrasted with the glorious beginnings of Rome.
The Romans saw themselves as the most successful people of the world and to trace the 'Roman miracle' (which it was), how did a small village along the Tiber grow to dominate the known world? Livy gives the antecedents for this present imperial glory to the ancestors, that they owe everything to the mos maiorum and delineates the national character (romanitas). But much of the early history is rooted in myth and legend. But archaeologically we know Rome was a powerful monarchical state. Livy himself is aware of his tenuous grasp of his history.
We start with Troy - so Rome was already tied in with Greek history whose history also led back to Homer (Herodotus attributed the abduction of women by Greeks and Persians which led to Helen and the distant origin of the Persian Wars). Aeneas fled Troy and founded Lavinium which brought conflict with the indigenous people (and his marriage to Lavinia). A treaty is reached and the various people take a common name: the Latins.
Aeneas eventually died and was deified; his son Ascanius would found a new settlement, Alba Longa. Ascanius is said to have an alternate name of Iulius which tied into the Julii's claim of descent from Venus (Aeneas’ alleged mother). So