It is also important to look at how names are written in contemporary documents. For people in the lower classes double surnames we’re uncommon in the older records, and we’re much more common in the upper classes, but by far from universal. Modern records are different, where double surnames are very common, but still not universal.
In the older Mexican records it is sometimes difficult to tell if people identified as Indian in the record had a surname of not. Names simply like Juan Diego or Maria Teresa are common, and likely were without a surname. Later names for Indians like Juan de la Cruz, or Maria de la Trinidad, were quite common, where de la Cruz, or Cruz, eventually became the surname.