Hey Mike, a bit of additional advice, since a lot of us are dealing with unknowns, and many of us have also been bitten in the ass with half-ass/lackluster labeling.
Any time you see someone writing "Celeste strain" or "Celeste variant", it could be any number of things. The entire LSU breeding program (interesting read, see: O'Rourke and his figs) was based around crossing Celeste with other stuff, and cuttings from those research beds have leaked out over the years, varieties have been named and sold ..... O'Rourke, Improved Celeste, LSU Tiger, LSU Purple, etc.
So, in the case of the fig posted in this thread, I would probably label it: "Celeste?". If you want to get rid of the question mark on the tag, keep coming back to this thread and updating with pics of the fruit as it ripens, take pictures of a few of the different leaf shapes, maybe some pics of the eye of the fruit when it's still small and green, or even leave a few to hang on the tree to see if it has traits of specific strains - the way the skin wrinkles or cracks, the flesh color, etc. Knowing you're in CT is helpful also (that info isn't in your profile), because ... well, Celeste has completed ripening in Atlanta, but others in your vicinity may confirm that a specific Celeste strain/variety they have is ripening at the time you're posting pics, ripening times for your zone are also an ID point.
With the above info, someone here is bound to link it to a named variety in their collection, and you can better refine your tag.
In short, "Celeste" is a good ballpark, but not a definitive ID per se.