I'm guessing now it's the same as Spanish because of imperialism, but did Catalan names originally follow the First name + Second name + Father's surname + Mother's surname naming system?
Yes, nowadays we use both surnames. We can't be sure of what would have happened, but the two surnames we have now were a Spanish imposition in most cases.
Before the 19th century, most Catalan men used only one surname. Only the upper classes had more surnames, since they often wanted to keep stacking titles (think of those really long names of nobles, if you marry into another powerful family and yours is powerful too you wouldn't want either of the lineages to get lost, the most titles you can "collect" the better!). Women could often use two surnames after getting married (their father's and their husband's).
In 1870, the Spanish law decided that civil register should have 2 surnames (first the father's and secondly the mother's) for each person to identify them better. That's how people started to have two surnames.
The most visible effect of this law, however, is the spelling. When Spanish-speaker state officers had to write down Catalan surnames, they would write them down according to Spanish spelling rules. That's why many Catalan surnames have a "Spanishified" spelling, like "Peña" instead of Penya, "Calzada" instead of Calçada, "Lladó" instead of Lledó, etc.
(As for first names, usually we only have 1 except you've been baptized, but that's not an official name and how much those 1 or 2 extra names are counted as part of your name depends on each person or family)
More information about the origin of Catalan surnames below the cut.
In the Middle Ages, Catalans had a name and a "nickname", often referred to a characteristic. Many of our surnames come from here. For example, physical attributes like Roig ("red", red-haired), Tort ("hooked"), Petit ("small"), Rossell ("blond"), Calvet ("balding"), etc; or jobs like Ferrer ("blacksmith"), Fuster ("carpenter"), Carnisser ("butcher"), Oller ("potter"), etc.
Among Catalan people, the use of surnames started being generalized in the 9th century.
In legal documents of the time, we see people are referred by who their father is. If the text was in Latin (even though people already spoke Catalan, Latin was still the most used language in writing), the first name would be in nominative case and the father's name in genitive case; if the text was in Catalan, it would be after the preposition "de", meaning "of" (same meaning as the cases in Latin). For example, Berenguer son of Ramon was Berengarius Raimundi in Latin and Berenguer de Ramon in Catalan.
Genitive case often ends in -is, that's why in Spanish and Aragonese you can find lots of surnames that come from a name+ez. For example: Sánchez would be the son of Sancho, Hernández of Hernán, López of Lope, González of Gonzalo, Rodríguez of Rodrigo, Martínez of Martín... Even nowadays, in Spain, 14 out of the 17 most common surnames are a name+ez! (Source)
This is not the case in Catalan. This Latin-derived surnames didn't become used. We only have 3 surnames with this origin (Peris, Sanxís, and Llopis) and they arrived to us from influence of Aragon, Castile and Navarre. Besides, neither of them is very common, unlike their Spanish equivalents. There was an exception in the Valencian Country, because some areas had a lot of Aragonese people as well as Catalan people or at least a strong Aragonese influence, so there existed more surnames related to the Aragonese ones.
From the 11th century on, the nobles started using the name of their lands as a surname, either after "de" (de Barcelona, d'Empúries...) or in adjective form (Barceló, Tarragó, Giró, Tàrrec). This started in the nobility to know who inherited what territories, but it was soon followed by the lower classes as well.
Lower class people often didn't have a territory to refer to and so they would use a name that made reference to their farmhouse, where they live, or other geographical terms. From here we get many of the most common Catalan surnames such as Riera ("stream"), Torrent ("watercourse"), Puig ("hill"), Pujol ("hill"), Vall ("valley") or Valls ("valleys"), Coma ("mountain pass"), Pomar ("apple orchard"), Vinyes ("vineyards"), Rovira ("oak tree forest"), Ribes ("shores") or simply the names of towns or areas like Solsona, Bages, Segarra, Agramunt, Vila, Canet, Cardona, Cabrera, Güell, Barberà, Cerdà...
All of this applies to men, but it worked differently for women because they weren't considered carriers of lineage in the same right as men, and were seen as under the property of a man (father or husband). In the Middle Ages, Catalan women usually had a feminine version of the father's surname (for example, if the father is Ferrer, she would be Ferrera). After getting married, women sometimes had both the father's and husband's surnames or only the husband's.
Source: Janer Torrens, Antoni (2014), "L'origen dels noms i cognoms catalans. Les arrels antroponímiques que marquen una identitat", II Congrés de la Societat d'Onomàstica i la XXVII Jornada d'Antroponímia i Toponímia de la UB. PDF.