She was a Spanish princess by birth. So why is she called "of Austria"? Is it because her mother was an Austrian princess? But presumably, it should be the person's place of birth that gives them their sobriquet, not their parents'.
Come to think of it, is the name "Anne of Austria" even contemporarily attested? Or is it a later appellation, not used during her lifetime?
UPDATE As @Semaphore has now convincingly showed, Anne really had the title of Austrian Archduchess (something baldl asserted in wikipedia, but not sourced there). Still, we need to find out why the "of Austria" became her standard sobriquet.