My take on the D.'s... possible spoilers although most of it is really just conjecture.
During the Void Century there was a large, technologically advanced Kingdom which no longer exists. How and why it vanished is something the World Government wants to keep under wraps, to the extent of destroying Ohara for researching it. We know that the "Will of D" is connected to the Void Century from what Rayleigh said. And D is a name passed down through the generations, often in secret, as is the case with Law. In fact, the WG actually called Gol D. Roger "Gold Roger" to cover up the fact that he is a "D." And now we have, in the most recent chapter, Corazon telling Law that he needs to get away from Doffy - a descendant of the original founders of the World Government, which was founded right around the time when that kingdom disappeared.
So why is the name kept secret, and what does it mean? My guess is that it's passed down from survivors of the lost Kingdom, to keep their history and their people's will alive, and to eventually expose what did happen during the Void Century. Which is probably that the WG did some seriously heinous shit, which if known would completely undermine their authority.
I have an idea that the Devil Fruits are inventions of the lost Kingdom as well, and were dispersed by the Kingdom when the end was near so people would be able to gain the power to fight against the WG after they were gone. After all, Vegapunk has made artificial Devil Fruits, and he's basically just one guy doing it.