Yes, the inscription translation is correct. Nakatani is the family name, and Kamatarō is the first/given name.
Sorry to say that Nakatani is a somewhat common last name, so it would be extremely difficult to trace the descendents of the original owner of this sword. Equally impossible to determine what his exact social status was, but you can imagine he was someone with some wealth since he could afford the sword, and could afford the special inscription on it.