It depends. Normally book tickets as your name appears on the passport you are going to use.
I have the same dilemma - in Mexico, FIRSTNAME PATERNALSURNAME MATERNALSURNAME is the norm, in the US where I reside and have a passport, it's FIRSTNAME MIDDLENAME PATERNALSURNAME or whatever one is using as such. The US airlines are likely to bend it - my sister is FIRSTNAME PATERNALSURNAME-MATERNALSURNAME, both shown as one name in the SURNAME box.