Wiktionary.de gives several theories, the first of which is that the name does indeed come from an archaic form of "eastern empire" :
Herkunft:
[1] um 996 n. Chr. als Ostarrîchi bezeichnet, was sich wahrscheinlich aus der damaligen Bezeichnung für Osten und dem Begriff für eingegrenztes Gebiet (-rîchi) ableitet. Es gibt auch Theorien, dass sich der Name Österreichs von dem Namen Ostara, der germanischen Göttin des Frühlings und der Morgenröte (Osten) ableitet oder aber slawischen Ursprungs ostarik, ostrik - Spitzberg ist.
Wiktionary.de gives several theories, the first of which is that the name does indeed come from an archaic form of “eastern empire” :
Herkunft:
[1] um 996 n. Chr. als Ostarrîchi bezeichnet, was sich wahrscheinlich aus der damaligen Bezeichnung für Osten und dem Begriff für eingegrenztes Gebiet (-rîchi) ableitet. Es gibt auch Theorien, dass sich der Name Österreichs von dem Namen Ostara, der germanischen Göttin des Frühlings und der Morgenröte (Osten) ableitet oder aber slawischen Ursprungs ostarik, ostrik - Spitzberg ist.
However, Friedrich Heer, one the most important Austrian historians in the 20th century, stated in his book Der Kampf um die österreichische Identität (The Struggle Over Austrian Identity), that the Germanic form ostarrîchi was not a translation of the Latin word, but both resulted from a much older term originating in the Celtic languages of ancient Austria: More than 2,500 years ago, the major part of the actual country was called Norig by the Celtic population (Hallstatt culture); No- or Nor- meant East or Eastern, whereas Rig is the related to the modern German Reich; realm (among other things). Accordingly, Norig would essentially mean ostarrîchi and Österreich, thus Austria. The Celtic name was eventually Latinized to noricum, when the Romans conquered and Romanized the country that later became Austria. The name of Noricum was then used to designate the Roman province.
According to Herr, originally Österreich comes from Celtic words meaning "Eastern Realm or Kingdom."
I don't know if that's true, but the Ostara theory has a Nazi ring to it. Ostara was the name of a magazine that may have influenced Hitler.
The reference to Latin is interesting: "Austria" comes from the Latin word for "South", even though the Germanic and Celtic names (and Noricum, which the Romans called the area) had nothing to do with anything Southern.