This is the $2 fig tree i got from Home Despot about 18 months ago.

last winter it still had fruit trying to ripen in December.
sadly, they failed, or all tasted bad.
the 1 fruit that ripened in the fall, wasnt very good either.

actually, this is the 2nd fruit... the first was a breba about a month ago.
i didnt get to taste it though.

i was hoping some iron and magnesium and fertilizer
would make the fruit taste better.
it appears not really.
while it had some sweetness, the skin was very thick
and not much flavor besides.

i has rained for 10 out of the last 12 days
maybe that is diluting the flavor ?
i might just have to wait another month or 2
and see if i get better tasting fruit.

i might try to graft to it. its a fast growing tree,
with lots of fruit, almost all year long.

can anyone pin a name to it ?

Looks like Italian Honey(Lattarula). They are pretty common and have a clear syrupy interior.

http://www.burpee.com/fruit/figs/fig-lattarula-italian-honey--prod100082.html

I have a similar unknown green fig tree with figs ripening now, never thought it was any good. It may be a Lattarulla variation. Then some forum members advised me to let it stay on the tree until it had brown spots. Fully ripe it has a nice jammy white sugar taste that isn't bad, especially when it's the only fig around.