1. The personification of the city of Rome, and as such called Dea Roma. Temples were erected to her, not only at Rome, but in other cities of the empire, such as Smyrna (Tacticus Annals iv).
She was represented clad in a long robe, and with a helmet, in a sitting posture, strongly resembling the figures of the Greek Athena. She was in reality the genius of the city of Rome, and was worshipped as such from early times; but it seems that previous to the time of Augustus, there was no temple dedicated to her in the city; but afterwards their number increased in all parts of the empire (The The History of Rome By Titus Livius. xliii).
As Roma also signified "strength," it is not impossible that the ode of Erinna, addressed to Roma, may be an ode to the personification of strength.
2. A Trojan captive, who advised her fellow captives on the coast of Italy to set fire to the fleet of the Greeks. (Plutarch, Romulus; Tzetzes on Lycophron)
3. A daughter of Italus and Lucania, or a daughter of Telephus. In some traditions she was said to have been the wife of Aeneas or Ascanius, and to have given her name to the city of Rome. (Plutarch, Romulus)From Smith's Dictionary of Greek and Roman Biography and Mythology
From The Non-Christian Cross, by John Denham Parsons
Nepotianus, a nephew of Constantine the Great who took Rome in A.C. 350 but was killed as an usurper the same year, issued a coin on the reverse of which, surrounded by the legend Urbs Roma, is a female figure representing Rome and holding in her hand a round object surmounted by the symbol .
The symbol frequently occurs upon the coins of Valeus (A.C. 364—378). And upon one coin of this Emperor we see the letter Ρ surmounting a cross; surrounded by the legend Gloria Romanorum.
From Lives of the Noble Grecians and Romans By Plutarch. Romulus
From whom, and for what reason, the city of Rome, a name so great in glory, and famous in the mouths of all men, was so first called, authors do not agree. Some are of opinion that the Pelasgians, wandering over the greater part of the habitable world, and subduing numerous nations, fixed themselves here, and, from their own great strength in war, called the city Rome. Others, that at the taking of Troy, some few that escaped and met with shipping, put to sea, and, driven by winds, were carried upon the coasts of Tuscany, and came to anchor off the mouth of the river Tiber, where their women, out of heart and weary with the sea, on its being proposed by one of the highest birth and best understanding amongst them, whose name was Roma, burnt the ships. With which act the men at first were angry, but afterwards, of necessity, seating themselves near Palatium, where things in a short while succeeded far better than they could hope, in that they found the country very good, and the people courteous, they not only did the lady Roma other honors, but added also this, of calling after her name the city which she had been the occasion of their founding. From this, they say, has come down that custom at Rome for women to salute their kinsmen and husbands with kisses; because these women, after they had burnt the ships, made use of such endearments when entreating and pacifying their husbands.
Some again say that Roma, from whom this city was so called, was daughter of Italus and Leucaria; or, by another account, of Telephus, Hercules’s son, and that she was married to Aeneas, or, according to others again, to Ascanius, Aeneas’s son. Some tell us that Romanus, the son of Ulysses and Circe, built it; some, Romus the son of Emathion, Diomede having sent him from Troy; and others, Romus, king of the Latins, after driving out the Tyrrhenians, who had come from Thessaly into Lydia, and from thence into Italy. Those very authors, too, who, in accordance with the safest account, make Romulus give the name to the city, yet differ concerning his birth and family. For some say, he was son to Aeneas and Dexithea, daughter of Phorbas, and was, with his brother Remus, in their infancy, carried into Italy, and being on the river when the waters came down in a flood, all the vessels were cast away except only that where the young children were, which being gently landed on a level bank of the river, they were both unexpectedly saved, and from them the place was called Rome. Some say, Roma, daughter of the Trojan lady above mentioned, was married to Latinus, Telemachus’s son, and became mother to Romulus; others, that Aemilia, daughter of Aeneas and Lavinia, had him by the god Mars; and others give you mere fables of his origin. For to Tarchetius, they say, king of Alba, who was a most wicked and cruel man, there appeared in his own house a strange vision, a male figure that rose out of a hearth, and stayed there for many days. There was an oracle of Tethys in Tuscany which Tarchetius consulted, and received an answer that a virgin should give herself to the apparition, and that a son should be born of her, highly renowned, eminent for valor, good fortune, and strength of body. Tarchetius told the prophecy to one of his own daughters, and commanded her to do this thing; which she avoiding as an indignity, sent her handmaid. Tarchetius, hearing this, in great anger imprisoned them both, purposing to put them to death; but being deterred from murder by the goddess Vesta in a dream, enjoined them for their punishment the working a web of cloth, in their chains as they were, which when they finished, they should be suffered to marry; but whatever they worked by day, Tarchetius commanded others to unravel in the night. In the meantime, the waiting-woman was delivered of two boys, whom Tarchetius gave into the hands of one Teratius, with command to destroy them; he, however, carried and laid them by the river side, where a wolf came and continued to suckle them, while birds of various sorts brought little morsels of food, which they put into their mouths; till a cow-herd, spying them, was first strangely surprised, but, venturing to draw nearer, took the children up in his arms. Thus they were saved, and, when they grew up, set upon Tarchetius and overcame him. This one Promathion says, who compiled a history of Italy.