If you search my posts, they are mostly about identifying a fig tree I have.  I've searched many sites and asked many fig collectors about my fig, but it doesn't appear to be an obvious variety.  I'd like to start selling cuttings locally and on Ebay, and also start trading my variety, but was wondering if I may simply give it a name of my own, along with the background history of the plant.  I have nearly 600 feedback on Ebay with 100% positive, so I know what it takes to sell an item.  The #1 way to be a respected seller is to be 100% HONEST about what you're selling.  My main concern with selling fig plants is that I don't want to break any rules with naming.  I'd give it a name that doesn't already exist.
But for those interested, I was chatting with my parents yesterday and got a lot more info on where the family fig tree came from.  My grandparents moved to Cleveland from Carini, (Province of Palermo) Sicily in the late 60s and my grandfather was given cuttings from a cousin, who also lived in the same area.

There are no rules.

If you have a seedling, then it is new and unique, like your first born child, and thus has no name, and you get to do the honors.

Yours, having come from Carini probably had a name at one time. It may exist there, and here (brought by someone else) by its original name, or some other name (Luigi's Gold, or whatever). Since it is really hard to identify figs (they look different when grown in different places) you may never identify it. So, give it a name that preserves its past and is descriptive of what it is, and pass along the story of its origin when you share/sell cuttings. So call it Carini Black, or Fico Carini or some such name (I don't known what the color of this fig is). There are a ton of "Unknown Italian" figs, so give it a real name. Can't argue with just being honest about it when you are selling it. It would be nice if more people were.

Thank you so much for responding.  I was hoping someone in the business would reply.  I feel much better now.  Funny how attaching a name to an unknown makes it that much more special (to me).  Thanks again, and I'll be actively trading/selling cuttings in a month or two.