I don't want to be the bearer of bad news but you can't change the name on those code share rewards flight.
We made the mistake last year - EK and QR J rewards then a number of paid cash flights.
My wife ended up reissuing her passport back into her maiden name (for a fee) so we could travel with her maiden name as booked on the flights.
Please make sure they get onto this with urgency as it's not a pleasant experience when you realise. There's a few stories online of people being caught out by this too.
Changing your name when booked direct is generally fine, classic reward on QF metal is fine too - it's the code share redemptions that you can't.
FWIW bringing documention is not enough for an international flight, boarding pass must match passport and they will probably be denied boarding.