The most comprehensive DNA testing done so far on fig varieties can be found in this document:
Jon posted about it in this thread:
They tested 194 varieties from the UC Davis collection. They found some to be duplicates.
Here's what makes this so difficult. Every new seedling grown from a pollinated fig (where the wasp and caprifig exist) is a genetically unique individual and is its own variety. Because of this I am sure that there are thousands if not tens or hundreds of thousands of varieties of figs out there. They've been in cultivation for thousands of years. Every little village in Southern Europe and the Middle east has some figs that are unique to that area. The number of fig varieties is pretty mind blowing.
Here we are in America cut off from the historical and geographical continuity that exists in Southern Europe and the Middle East and we're trying to connect the dots and figure out what the variety is and where it came from originally.
What we really have to guard against is assigning duplicate names to varieties that are already in circulation over here. That is something that we can control and do something about. But I don't think we'll ever be able to find the original variety name to a fig that some guy brought over 80 years ago from his little village in Italy or Greece.
I have reservations about adding "Unknown" to the name of a fig. Every new fig is going to be Unknown This and Unknown That. That seems to make it even more confusing. Before you know it there will be 80 Unknowns and everyone will be confused by that.