What does the Machine Readable Zone (MRZ) at the bottom of the picture page of the passport show (this is what the agents scan when they check you in)?

Note that the "<<" is what distinguishes your surname from your other names, prefixes, suffixes etc.

#1 DOE<<JOHN

#2 DOE<<JOHN<III

#3 DOE<III<<JOHN

If #1 or #2, ticket should have at minimum DOE/JOHN

If #3, ticket should have at minimum DOE III/JOHN OR DOE/JOHN III