Yes, one of the names is Shirazi, which might be a name that encompasses one of the regions in Iran where they are grown. There have been some other posts about these figs and there was a good link mentioned above. One major growing area is Estahban. If you do a Google Images search on "Estahban Figs" you will find some nice images and other information. One of the specific varietal names is Sabz and there are others.
I grew some from seed - mostly just for fun since there is almost no chance any of them will turn out to be a common fig type. They will either be caprifigs or a Smyrna type. Another good reason to grow them from seed is to get virus free rootstock in case you are doing any experiments along those lines.
Regarding the male/female genetics and persistent/caducous genetic issues, take a look at post #13 here.
By the way, those "Shirazi" figs are quite tasty. They are small dried figs but pack in a lot of flavor.
Take care,
Byron (Ingevald)