Quite an interesting subject, this.
My one cent contribution.
For most of us, names become important when trading cuttings. For some it is absolutely necessary if selling figs on ebay, for example.
I think that as long as the fig with no pedigree is amply described and a brief history is available it could be given a temporary name.
For example, the cuttings that I obtained on my travels to Europe and Morocco obviously do not have names. But even for purposes of putting a label on the potted plants it is necessary to give them a name.
My large white fig from Cucchiano, Rende, Cosenza, Calabria, Italy is simply labeled White Cucchiano. Should I ever offer cuttings, it would come with a full description of the tree, fruit, taste etc as well as a history of where the cutting came from (ie my childhood home and the memories associated with it).
As long as no one tries to pull the wool over someone's eyes by misrepresenting the fig, I think it is OK.