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A name was never given for the country that they're in. Jun even stealthily eluded having to name the country which Isla Yura, Rufus Barma and the rest of the Barma family originated from. They were simply Isla Yura's country, and Pandora's country.

However, because Pandora Hearts takes place sometime in the Victorian age, it is set somewhere in Europe. Now, the Barma family are said to come from a background which had the instrument the morin khuur, which is a Mongolian instrument, however the only European country close to Mongolia is Russia (which is technically Eur-Asian). As well, many names throughout the series draw inspiration from different languages, such as Marie (French origin), Rytas (Portuguese for 'Morning') the villiage of Toll (German for 'Gate') the Carrillon region (French for 'Chime'), Zwei (German for Two), Sablier (French for 'Hourglass'), Reveille (French for 'Wake Up') etc.

While Pandora Hearts' main setting does appear to be similar to Russia and Mongolia while drawing aspects from other cultures as well, one must remember that Pandora Hearts is fictional, meaning that it could be Jun's intention to make the series take place in a made up country.