While we may find the name of Khafr, a region between Shiraz and Jahrom, in the inscriptions of Darius the Great, there is no mention of any important town in the Pars region, during the Persian Empire (B.C. 600-330).
As for Parthians dynasty which expanded the City of Ctesiphon on the Tigris River and ruled Persia (Iran) for about five hundred years after defeating the successors of Alexander, there remains nearly nothing to give us a historical hint on any town or region during their reign, thanks to the hostility of Sassanids who toppled down Parthians and annihilated all written relics of their historical rivals.
It is then quite impossible to discover the early history of Jahrom beyond Sassanid Period. And the relic of a Zoroastrian Fire-Temple overlooking Jahrom from a hill top has the profound sign of that epoch.
Based on Ahmad Kasravi, the late Persian historians and philologist, the name Jahrom can be analyzed to render a "warm-place". But a more satisfactory etymology interprets the name as a "green-place" (see the Etymology of Jahrom):
The name of the town appears as Zarham in the Chronicle of Artaxerxes [Karanamak-i-Artaxshir Papakan], the founder of Sassanid dynasty, which if accepted, takes the history of Jahrom as far back as 2nd century A.D. The name later appears as Jahrom in Firdausi's Book of Kings [Shah-Name].; and can be cited in 5 different verses in the epic.
Currently, Historians believe that Jahrom, as a garrison, was conquered by Arabs soon after the Sassanids capital, Ctesiphon , was plundered by them in 637 A.D. On the other hand, Dr. Ali Hasoory, a Persian historian who has thoroughly examined the ancient Sassanid coins, is of the opinion that the last Sassanid king Yazd-Gerd did not escape to "Marv" in the North East of the country (near the Caspian Sea, where he was assassinated: a story quite ironically similar to the fatal destiny of Darius III, after defeated by Alexander) but retreated to "Marv-dasht" in Pars, where he founded his second court to stand for another 55 years. So pars and other strongholds in the region (such as Jahrom) resisted for half a century before yielding completely to Arabs.
In any case, the name of Jahrom's governer at the time of Arab invasion has been recorded as Farrokh-Zad, and he is supposedly the one who lead the Persian army.
The most famous Jahromian we know from the ancient times is Barbad, the troubadour who became the main lyricist and musician in the court of the great Sassanid king Khosrow Aparviž (Parviz).