It's part of the culture of growing figs in my opinion, especially if you're not renaming a known fig cultivar on purpose. Examples that come to mind- Figo Preto, Hardy Chicago, JH Adriatic, Cravens Craving, Brooklyn White, etc. without a name it's just another black fig.
In contrast, there was a guy in New Mexico who had a huge collection of unknown figs he had found locally and never named. He just described them as black or green ,etc. He tried to sell his little local fig nursery a couple of years ago on Craigslist and I think he's done figging but just imagine the great varieties he could have introduced if he just named a couple of his best figs.
Which would you prefer- a bunch of "green" or "black " figs in your collection or names that distinguished them?
Just my 2 cents.