Anne of Austria or of Spain?

Anne of Austria was the wife of King Louis XIII of France.
Though called Anne of Austria, she was the daughter of King Philip III of Spain.
Why is she not referred to as Anne of Spain?
 
Anne's niece, Maria Teresa of Austria was the wife of King Louis XIV of France.
Though called Maria Teresa of Austria, she was the daughter of King Philip IV of Spain.
She was of the House of Habsburg of Spain.
 
Considering that the Habsburgs were called in Spain as House of Austria, there is no problem at all about calling her Anne of Austria.
 
Am I crazy or did not the house of habsburghs came from Aústria?Din´t Charles V divede it´s empire between his son Felipe(future king of Spain) and his brother?Because TO me it certainly looks like the same family.
 
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