I believe an Amora in the Gemora is referred to as “Baghdadi”. Is that the same Baghdad as today?
When did the Yidden from Bavel — mostly — move out, and to where?
Sura is now called Fallujah
The most significant Jewish, Torah based population was in Bavel and/or Persia from 11 years before Churban Bayis Rishon (Hecharash v’hamasger) until roughly the time that Rabbeinu Gershom left and went to Europe. The greatest gedolim and biggest yeshivos were mostly (but not completely) in Bavel. Rabbeinu Gershom, upon moving to Europe about 50-100 years before the birth of Rashi, became the first Gadol Hador to live there. Rav Hai Gaon was probably the last of the Gedolei Hador to live and die in that area.
The Ben Ish Chai quotes I-forgot-who that Pumpadisa and Nahardaa is where Bagdad is now, and Bagditaha is something else. If I recall correctly, he says that the name of the city was in fact Bagdad, but the Yidden gave it their own name.
midwesterner: What is your source for that history. Particularly that Rabbeinu Gershom moved from Bavel to Europe, rather than haven been born in Europe, and that he was the first godol to do so. And that Rav Hai Gaon was of the last gedolim to die in Bavel.