A¬†recurring question I have encountered by students in Melbourne; why do¬†Austrian¬†number plates display ¬†A for Austria, even though their countries German name is Österreich?
"Ostarrîchi" (Old High German language) is the linguistic ancestor of Österreich. It means " Eastern realm" and refers to the lands position in relation to the other German speaking areas. The Old High German word for Austria  first appeared in writing in the Ostarrîchi document (a parchment document written in Latin) of 996, where it refers to an area located mostly in what is today Lower Austria. Old High German language was used between mid 9th and mid11 th century. Öster= oestlich; "eastern" (der Osten;  "the East") Reich; "realm, dominion, empire".
The term idea of Eastern Realms might have originated in a translation of the Medieval Latin name for this region: Marchia orientalis. It translates as "eastern marches" or "eastern borderland" and was situated at the eastern borders of the Holy Roman Empire (Heiliges Roemisches Reich in German). The first recorded use of the Latin word Austria was in 1147.  The latin term "terra orientalis" was replaced with Austria, maybe to show the difference to the Eastern Empire which was by then in Byzantine.
So, despite researching this topic I have found no solid information to support me, yet suspect that Austria uses "A" based on the Latin name for it's country - Austria. Switzerland is another country where this is the case, with its symbol being "CH" which is derived from its Latin form "Confoederatio Helvetica".