There are some varieties which are fairly distinctive, such as Panache, which makes them easy to identify. Beyond that, because figs respond, often dramatically, to most elements of their environment, visual identification is very difficult. If you looks at the pix of the collection at WEO (USDA at Davis) over the years, (the last couple of visits are not ready yet), you will see the wide variations in the fruit from year to year, esp. in skin color.
You can do DNA testing, which will tell you if it matches a variety whose DNA has already been tested, but there are few that have been tested, outside of collections such as the USDA collection.
After you have matching DNA, you may still not have the entire story. The level of DNA testing may not disclose nuances which are observed in different "variants" or "strains" of the same variety, which can affect fruit size, color, etc.
Many figs are "discovered" in backyards and other places and there is no history of what there name is. They get a variety of names depending on the "discoverer". I choose to name mine for the streets they were found on, to give them a semblance of a provenance. Some use Unknown with a town name or other moniker. There aren't any rules. Probably the only really bad approach is to think that you can be certain of what you unknown is after comparing a few pictures and start calling it by that name. I have figs from east coast nurseries that the people I bought them from do not recognize when grown here in paradise.
In the end, if it tastes good, name it Tom, Dick, or Harry, but share some with me. I'm all about flavor.
Welcome to the "fun" that is figs.