Who the other 6 were exactly is unknown.
As you said, one of the rings was given to Durin III, known as the "Ring of Thror", and was passed down the line of Durin for thousands of years before Sauron recaptured it in the Third Age, during Thrain II's capture in Dol Guldur. As for who the other rings belonged to, the most we can go by is that they were "Dwarf-kings" and most likely the kings of the Seven Houses, as said by Gandalf:
Seven the Dwarf-kings possessed, but three he has recovered, and the others the dragons have consumed.
The Lord of the Rings, The Fellowship of the Ring, Book I, Chapter II, A Shadow of the Past
It is also worth noting from the above quote that three were recovered by Sauron, including Thror's Ring. That means 4 were consumed by dragons, between their coming in T.A. 2570 and T.A. 2845 when the last ring, Thror's Ring, was claimed.
There, unfortunately, isn't much else written about the Seven Rings and who received them, when they were lost and how they were taken.
An interesting read speculating on how Sauron gave the Seven Rings to the Dwarven kings was written by Michael Martinez, the renowned Tolkien scholar, on his blog.