Traditionally, Chileans and many other Latin Americans use double surnames to identify themselves; a child takes both the paternal and maternal surnames, in that order.Salvador Allende Gossens , the late president, took the name Allende from his father’s side, while Gossens comes from the mother’s. Normally, Salvador would go by the surname Allende, but he would sign legal documents as Salvador Allende Gossens. After marrying Salvador Allende, Hortensia Bussi Soto  became Hortensia Bussi de Allende. Their daughter Isabel, a current Chilean senator, goes by the surnames Allende Bussi (the California-based novelist Isabel Allende Llona is their niece) . Hortensia’s own surname would be lost in the succeeding generation.
There are exceptions even to these rules, especially when elite families want to retain conspicuous evidence of their heritage - the late president Eduardo Frei Montalva  (pictured above, 1964-1970) married María Ruiz-Tagle Jiménez , whose hyphenated first surname dates well back into Chilean history. The children of their son, former president Eduardo Frei Ruiz-Tagle  (1994-2000), have lost the prestigious Ruiz-Tagle surname, however.
Aside from knowing which surname to use when dealing with locals, visitors to Chile may find a more practical application - don’t be surprised to hear Chilean officials, at border posts or elsewhere, call out your middle name on the assumption that it’s really your father’s surname.
Customs differ in Argentina, where the double surname is unusual, but that may be changing. According to the Buenos Aires daily Clarín, 40 percent of all new births in the city now bear the names of both parents  - representing a 76 percent increase over the past decade. On one level, in this regard, it would appear that Argentina is conforming more closely to Latin American customs; on another, it would seem to acknowledge a greater equality between father and mother (though the paternal surname always comes first). My late mother-in-law, an Argentine of Spanish descent, used her husband’s surname Massolo rather than her birth surname of Rodríguez; my wife uses the Italian-derived Massolo rather than a hyphenated Massolo-Rodríguez. Our daughter, born in California, uses the hyphenated but rather awkward surname Bernhardson-Massolo, which she signs “B-M” in the interest of brevity.
In either event, the result would appear to be a greater measure of legal equality between the sexes and within the family. It’s perhaps worth adding that, according to Portuguese naming customs, the maternal surname comes first, followed by the paternal surname.