There is an article on Spanish naming customs here -
http://en.wikipedia.org/wiki/Spanish_naming_customsIf you read down you'll see a note on Argentinian names. It would appear that a formal Spanish surname requires both father's and mother's surname, father's name first, but an Argentinian only needs one surname.
However, it's not clear how a married woman would be known. In Spain a married woman keeps her surname but adds her husband's. In Argentina ... ?