Unfortunately, as Robert Ocasio pointed out, it depends on the country and timeframe, even after civil records where established in most of them and also of the type of doumentation you have available - church, civil or legal records.
For instance in my country, Argentina, in the 1800' to mid-1900', in both church and civil records only the fathers' last name would be used but in other documents both the father and mother's last names would be used. This was mostly done by the upper/middle classes (as a mark of their social status). Lower classes had only one last name - if any. Many descendants of african slaves and native laborers did not have a last name recorded until mid-1800'.
Other countries of Latin America were more consistent with the 1) form.
The 2) form is still used today in legal jargon, like inheritance documents.
Also since the Catholic Church (main religious influence in Latin America, up to the 1900') follows its own rules that not always match each country's laws, you may find that the names in church and civil records don't match exactly at times. EG:my mom was not baptized as a child because their parents were freethinkers, so when she wanted to marry my italian dad in church, she had to be baptized first, and the priest decided her first name was not "catholic enough" and used the saint of the day instead, so for the catholic church I'm the daughter of Victorio and Cecilia instead of Victorio and Roswitha.
PS: I'm sorry I can only add to the confusion...
