Say a dual New Zealand and Mali citizen is flying from NZ to Mali via Australia (pure hypothetical).
The passports are in different names. Mali passport alone needs transit visa for Australia. NZ passport alone needs a visa for Mali. Both passports together, in theory, do not need any visas.
In which passport should the flights be booked?
The crux of this question is the humble allegation that not only do airlines need to be sure that travelers are allowed to both the destination and stopover countries (requiring transit visas), but they also may need to have the details entered into ATIS or similar system. This can be a problem given that flights can be booked in one name/passport only.
This is not a duplicate of that question because that one does not deal with stopovers needing visa for one of the two passports.