"Your flight" refers to the holder with a 2nd-person pronoun whereas "Passenger Name" refers to them in the 3rd-person. So maybe "Your name" (sounds weird) or "Passenger flight" (label may be too long for the field beneath it?).

I don't see this as a huge issue. I would change the labels to simply "Flight" and "Passenger"

The labels are not parallel [0].

Something like ("Your flight" and "Your name") OR ("Flight number" and "Passenger Name") would be more grammatically consistent.

[0] http://en.wikipedia.org/wiki/Parallelism_(grammar)

I think he means if it says "your flight" it could also say "your name."

Those sections are for different readers, though. And at least I rarely need to be told my name in case I forgot.

If you haven't needed reminding of what your name is then you haven't been properly jetlagged ;)