Dear of troy: I have no doubt that you know how to make it. But you did not say how it got its name. There are many airborne yeasts that will make bread rise.The one that makes salt rising bread has to have a starter with some ingredients that help it, but it further requires some warmth that other yeasts do not, and the saltbox would pick up and hold just the right amount of heat to permit the proper yeast to incubate.
So putting the culture into the salt box gave the bread its name.