Why is austria named austria?

Austria derives its name from the Eastern March (Ostarrîchi), a frontier province established by the Bavarian dukes in the 10th century. The name Austria first appeared in a Latin document dated November 1, 996. The name Österreich is derived from Old High German Ostarrîchi: Ost-, "east", referring to the province's location relative to Bavaria, and -rîchi, "realm" (compare Modern German Reich). The name may also be derived from a hypothetical Old High German word Ôstar-rîhhi / Ôstarrîchi 'eastern realm', an old name for the Kingdom of Francia Orientalis.