@cendawanita @pilipinas @philippines That's correct, it originated from the Spanish. Pre-colonial “Philippines” didn't use family names / surnames. The closest found on record is similar to the European “son/daughter of” (although this one format is not common either, as far as surviving records are concerned).
Originally it was this format:
= “Paternal family name” y “Maternal family name”
Or, if a married woman:
= “Married husband's paternal family name” y “Unmarried paternal family name”
When the Americans arrived, they switched the position
= “Maternal family name” y “Paternal family name”
Or, if a married woman:
= “Unmarried paternal family name” y “Married husband's paternal family name”
Today: the Americanized Spanish format is still being used by the PNP (Philippine National Police) in mugshots, if I'm not mistaken.
Later, the Spanish “y” was replaced with a comma. More years later, a comma is also used to separate the “first name” (although not common, usually in forms), like so:
(using the example from the original post)
= Maria Jessica Jane, Kurios, Makiling-Cohen
Outside of filling-in forms, we just write: Maria Jessica Jane Kurios Makiling-Cohen. (Or, Maria Jessica Jane K. Makiling-Cohen.)
We naturally assume that the last two names “Kurios” (or “K.”) and “Makiling-Cohen” (using the same example) as “middle family name” and “last family name” respectively.
And it's natural to ask for “middle family name” here in the Philippines. ^_~