Upvote:2
As long as you have a valid passport that shows all your names the order of such name is not an issue for any airline anywhere in the world, it’s really only a challenge when they search for your name to find your ticket so make sure you have the booking number to ease the search. Even if you have multiple passports and dual citizenship its not a problem as long as names on the ticket corresponds to one of your passports that is valid for that travel leg.
I travel monthly to Ho Chi Minh in Vietnam from Shanghai China, two countries that are known for being picky with name vs Passport matching etc and I have on several occasions have my names switched on bookings so that my family name comes before first name or first and second name switched order etc. Never had an issue at any stage