Respecto a la cuestión de que si se le llamaba Babilonia a una ciudad o al país/región en el siglo I, es un asunto bastante complejo. No obstante, es importante señalar que si hacemos el análisis desde un punto de vista judío, es claro que Babilonia (Babel) hace mayormente referencia a la región/país y no a la ciudad en sí misma, pues siempre que se habla sobre los judíos en Babilonia es a todo el territorio, pues los judíos estaban diseminados en las ciudades y pueblos de dicha región, incluso ciudades como Sura y Pumbedita son sinónimo de Babilonia. Lo anterior es algo que ya se hacía desde al menos 5 siglos atrás (está claramente señalado en el Tanaj, ver Isaías 39:43 y 2 Reyes 20:14 (Son el mismo relato):
Isaías 39:3 Dios Habla Hoy (DHH):
3 "Entonces fue el profeta Isaías a ver al rey Ezequías, y le preguntó:
—¿De dónde vinieron esos hombres, y qué te dijeron?
Ezequías respondió:
—Vinieron de un país lejano; vinieron de Babilonia. "
De hecho durante la dominación Aquemenida Babilonia fue el nombre de una de las Satrapías (regiones administrativas).
Si deseas una mención en el s. I EC, entonces basta con ver lo que Flavio Josefo menciona en Antigüedades (XVIII, 4):
4. When the king had these intentions, he sent away Anileus, and Anileus prevailed on his brother [to come to the king], when he had related to him the king's good-will, and the oath that he had taken. Accordingly, they made haste to go to Artsbanus, who received them when they were come with pleasure, and admired Asineus's courage in the actions he had done, and this because he was a little man to see to, and at first sight appeared contemptible also, and such as one might deem a person of no value at all. He also said to his friends, how, upon the comparison, he showed his soul to be in all respects superior to his body; and when, as they were drinking together, he once showed Asineus to Abdagases, one of the generals of his army, and told him his name, and described the great courage he was of in war, and Abdagases had desired leave to kill him, and thereby to inflict on him a punishment for those injuries he had done to the Parthian government, the king replied, "I will never give thee leave to kill a man who hath depended on my faith, especially not after I have sent him my right hand, and endeavored to gain his belief by oaths made by the gods. But if thou be a truly warlike man, thou standest not in need of my perjury. Go thou then, and avenge the Parthian government; attack this man, when he is returned back, and conquer him by the forces that are under thy command, without my privity." Hereupon the king called for Asineus, and said to him, "It is time for thee, O thou young man! to return home, and not provoke the indignation of my generals in this place any further, lest they attempt to murder thee, and that without my approbation. I commit to thee the country of Babylonia in trust, that it may, by thy care, be preserved free from robbers, and from other mischiefs. I have kept my faith inviolable to thee, and that not in trifling affairs, but in those that concerned thy safety, and do therefore deserve thou shouldst be kind to me." When he had said this, and given Asineus some presents, he sent him away immediately; who, when he was come home, built fortresses, and became great in a little time, and managed things with such courage and success, as no other person, that had no higher a beginning, ever did before him. Those Parthian governors also, who were sent that way, paid him great respect; and the honor that was paid him by the Babylonians seemed to them too small, and beneath his deserts, although he were in no small dignity and power there; nay, indeed, all the affairs of Mesopotamia depended upon him, and he more and more flourished in this happy condition of his for fifteen years (Josefo, The Antiquities of the Jews, XVIII, 4).