It has been called "The surface" by Ghirahim, and several times it has been reffered to as the land below the clouds, in no interview has it never been mentioned to be called Hyrule. The exception is in an interview with Bill Trinen (see "Skyward Sword forging Hyrule interview" on Youtube.)
"Players will certainly get to go to some familiar places, but as to wether or not that's Hyrule or not Hyrule is something that will be explained over the course of the game."
I think this is pretty clear that we will get to see all the familiar Ocarina of Time and Twilight Princess locales such as Death Mountain, Lake Hylia, Gerudo Desert, and so on and so forth. But "something that will be explained over the course of the game" sounds to me as though it's not as simple as "People always lived in Skyloft, there was nothing before."
I think, that the inhabitants of Skyloft and the islands themselves were raised into the Sky by the Godesses to protect someone, someone important like, say Princess Zelda. I know Aonuma San has said that Zelda is in no way a princess in this game, and this altered my theory a bit. I think that since the people of Skyloft know nothing of a world below the clouds, they have been there long enough for the memory to have dissapeared from their culture, so there would have been several generations there already. I think that Zelda's descendant was a princess in the world below before Ghirahim took over. This might explain why he refers to Zelda as her "Holiness."
Maybe (Old) Zelda had something to do with the Triforce, and Ghirahim needs her to get it. What I have to support this, is that in Twilight Princess' movie after the Lanaryu Twilight is gone, the description of the Dark Interlopers that wanted to get their hands on the Triforce was I believe, skilled dark sorcers or something like that. I think that Ghirahim fits this nicely. But Aonuma San also confirmed that the Triforce takes on a different meaning in this game, by that he meant it isn't a story about the three pieces and Ganondorf trying to get all three.
I'm not sure, all I know is that the world below the clouds isn't called Hyrule, but it might of been before...