In my experience the airlines aren't fussed about the order of the names, just that the names on the ticket correspond to the names in the passport, irrespective of order. I was booked on MH and the agent had made the reservation Last Name/First Name rather than First Name/Last Name (or whatever way round it "should" be). I contacted MH who basically said what I've just commented. I have a partner who has both English and non-English names and two different passports. However the Australian passport incorporates the names on the other passport while adding further names. There's never been any problems with checking in. Nevertheless I wouldn't try it on a flight to the US