Wasn't country and western called hillbilly back then? Or maybe the name change occurred earlier. And how about bluegrass? Wasn't that hillbilly, as well?
I imagine that depended entirely on which part of the country you where in at the time. I believe folks in the south weren't to happy with the label of "Hillbilly" applied to their music. The Bristol sessions with the Carter Family were called "Folk" recordings and even Hank himself, in a rare interview, called himself a "folk" music writer.
I collect old radio recordings from that era. Programs like the Grand Ole Opry, Hanks' "Health and Happiness Hour", WLS National Barn-dance, etc.. never reffered to the artist or music as Hillbilly music. Often the Barn-dance announcer might say something like "bringing you the very finest in country and western entertainment".
I think the "change" form "hillbilly" to "country" music happened, like always, when it sold. When Hanks' song "Lovesick Blues" was a commercial success everywhere, and not just the deep south, folks up north started dropping the derisive term "Hillbilly" music, in favor of country music.
This is just like early blues recordings being called "race" records until they began to sell a little better.
as for the name "Bluegrass" referring to old time music...Bill Monroe coined that term entirely. The term itself (when used to describe music) did not exist until after Bill Monroe called his band the "bluegrass boys".