Full name, Middle name and Last name

I don't know to what end you mean the question, but let's guess you mean to a database (hence formal use). Depending on the database they would use a workaround way to add the middle name to either the first name or last name (or the family name/surname/lLast name).
It seems like they are now in some systems letting it be abbreviated
Tereza (first name) C. Melo (middle name) Dos Santos.

Sometimes they respect what the person wish and the usage in their country, when the person becomes famous/known by that name sometimes they may have chosen an unusual order.
Say, you are known by the compound "Tereza Cristina" rather than by "Tereza"
Not to extend much, let's take your name again, it could also be:
Tereza Cristina (ffirst name), Melo (middle name), Dos Santos (surname/last name/family name).

I read in a paper that 'patronymics and matronymics refer to the surnames of
Fathers and mothers respectively. The patronymic precedes the matronymic in all cases. Sorting by the final element when it is a matronymic would be in error", so when in doubt they follow the author wishes (in say, academical references, etc).

Ref. en.wikipedia
Ref. spanishindexing

I think we somehow follow the Spanish patterns there.