Let's assume my name is "A B C" for the argument's sake.
It's an Asian name, and it is written that way in the passport (more or less. Actually in the passport it is written with full phonetic marks and symbols - but is not unrecognisable from the non-phonetic one). The passport doesn't make it clear which part is the family, middle, and first name, it is understood that "A" is the family name, "B" is the middle name, and "B" is the first name.
I've booked an international flight, and the website requires to input names in order of first-middle-last. No problem here, I simply input them as they are. The problem is, when the ticket is issue, the name on the ticket will be "A/C B", unmatched with the one written in my passport. The name on the itinerary is "C B A", also not a match.
The reservation is already booked, and name change is impossible.
My gravest concern is with the given names. The whole given name as written in passport is "B C", while that on the ticket is "C B". Do you think it can be a problem?