It turns out that it not only seems that there are multiple systems, but there actually are multiple systems! So I feel somewhat justified in being confused. But I really want to learn this, not only out of linguistic interest but also out of wanting to be culturally sensitive to my students.
Here’s what Ancestry says:
For the most part, people now take the first of their father’s two surnames and the first of the mother’s two surnames as their own last name. Women sometimes add their husband’s surname to the end of theirs or in place of their mother’s surname, sometimes with a “de” between the two names. Therefore, a husband and wife generally have different sets of double surnames, as do their children.
In the past, however, Hispanic naming patterns were not as consistent. Sometimes, sons took the surname of their father, while daughters took that of their mother. The Castilian double surname naming system of the 16th century didn’t become common throughout Spain until the 1800s.
Confused yet? Just wait, there’s more!
Here’s what Culture Trip says about it:
[E]ven though the child inherits part of its surname from both its mother and father, it is always the part of that parent’s name that was given to the parent through their father which is transmitted.And the ordering of these names is not something that has been left to the parents to decide. Until 1999 the law stated that it was the father’s name which would come first in the ordering of the child’s surnames. Let’s imagine that Anna Martínez García and her partner Luis Sanchez Pérez have a daughter called Alexia. According to tradition, her full name would be Alexia Sanchez Martínez. However since 1999 a new law was introduced which states that the order of the child’s surnames can now be decided by the parents, although social convention means that many continue to list the father’s name first. And since 2011, an additional law states that each child can choose the order of their names upon turning 18 years old.
Although most Spanish people have two surnames, the custom is for them to only be referred by one of them when being addressed in everyday life. This is usually the first of the two surnames as they appear in writing, meaning that Anna Martínez García would usually be referred to as señora Martínez, and her partner Luis Sanchez Pérez would be referred to as señor Sanchez. This custom and the fact that most Spanish people have two surnames can sometimes lead to confusion in situations where people or companies that are not used to this system attempt to alphabetize names. The mistake made most frequently is to assume that the name that appears at the very end of the full name is the surname and to refer to that person by that name alone. In our example from above, Anna would be used to someone referring to her as Sra. Martínez García or Sra. Martínez, but not just Sra. García.
Women do not change their surnames upon marriage in Uruguay. In some instances, such as high society meetings, the partner’s surname can be added after the person’s surnames using the preposition de (of), but it is not a practice officially or legally provided, recognized or accepted.
Since 2013, parents may invert this order by mutual agreement, at the naming of the first child of the couple. Subsequent children must be named following the same order, since once the order of the surnames has been established it cannot be changed. If there is no agreement on the order, the rule shall apply depending on the type of couple: in case of heterosexual couples, the order shall be as in general practice (first surname shall be the paternal surname and the second surname shall be the maternal surname). Same-sex parents may choose the order of both surnames of the children (either from birth or adoption) by mutual agreement. In case of disagreement the order of the surnames is determined by draw.
For example, Natalia Marisa Oreiro Iglesias is the daughter of Carlos Florencio Oreiro Poggio and Mabel Cristina Iglesias Bourié. Note that the marriage between her parents did not mean that the mother lost her maiden surnames.
That last quotation is from Wikipedia, so take it with a grain of salt. It may or may not be correct. (There is a link to a citation, but it’s in Spanish, which I do not know, so I cannot verify the accuracy of these paragraphs.) And that’s just Uruguay. There are variations in other Spanish-speaking countries. And what happens when one parent is from one country and the other is from another? And how does Puerto Rico fit in? A lot more questions than answers here!
Next time maybe we’ll look at the surname-first question in Hungary, China, and a few other countries.