It was half in High Rock and half in Hammerfell. There were dozens of little kingdoms and principalities, almost all loyal to the Empire, and Daggerfall city was the capital of Daggerfall kingdom, but that was only a few percent of the total map area.
The second Elder Scrolls game, Daggerfall was also a city, actually pretty near Sentinel, just across the Illiac Bay.
Arena was supposed to be a nickname for the whole continent of Tamriel. Oblivion is a place, but most of that game was set in Cyrodiil.
So only two of the five so far, Morrowind and Skyrim, have been named after whole provinces.
For some reason I recalled that whole starting region in Daggerfall being called Daggerfall. I must be misremembering the map.
It was half in High Rock and half in Hammerfell. There were dozens of little kingdoms and principalities, almost all loyal to the Empire, and Daggerfall city was the capital of Daggerfall kingdom, but that was only a few percent of the total map area.