Supporters like to call their club Stern des Sdens ("star of the south"), as in their minds Bayern Munich represent the south of Germany. In Spain, Bayern are fearfully known as La Bestia Negra ("the black beast"). In the '90s, reporters started using a different nickname: FC Hollywood.
All Bavarians call their state Bayern & when they're speaking German. They might accommodate English speakers by using Bavaria a word that harks back to the Baiovarii, a tribe who settled there in the 5th century (and is probably Latin in origin).