The first time I travelled with my wife (then gf) I didn't know that she used her transliterated Chinese name on her passport and had booked tickets under her English first name. They were not too happy about it at check-in but it was resolved within about 5 minutes and they changed the return ticket for us.

Much more recently I mis-typed a W in her name as an H. They didn't even notice on the outbound but on return the check-in agent said we might have problems at the gate but nothing happened.

CX is much better about this than EVA who flat-out refused boarding over a simple typo in the passport number when booking online. One of the reasons why I gladly left EVA behind for CX.