I'd welcome advice on how CX and Hong Kong transit authorities will treat this situation:

Using my wife's AA miles, we have a CX award ticket for later this week, flying CX all the way from the USA to Hong Kong and transiting there to a destination in China. The potential problem, which I'd forgotten at the time of booking the tickets, is that her AA account name (and hence the name on her ticket) is somewhat different from her passport name in the following way:

Her AA account name (and ticket name): First name: Joan. Last name: Smith
Her passport name: First name: Joan. Last name: Green Smith (Yes, two words in the last name. "Green" is her maiden name).

FWIW, my ticket and passport name is: First name: John. Last name: Smith

Also FWIW, the passport name that CX has on file for her for this trip is correct: Joan Green Smith. (Just in case anyone has any doubts, I'm using illustrative names here rather than the real ones.)

When I just updated her travel document information regarding another matter (simply to include her country of residence and emergency contact), this message appeared:

Please note that one or more travel document names don't match the booking name, and this may cause delays at check-in and boarding. See the disclaimer at the bottom of this page on passengers' responsibility to provide accurate information. To change the name(s) on your booking, please contact us or the travel agency who made your booking.

In anyone's experience, is this a potential problem for CX or Hong Kong transit authorities, beyond the fact that perhaps she'll have to check in at the airport rather than online?

And if it is a problem, any advice on how to deal with it? I suppose if necessary we could change her AA name to match her passport and then try to change the ticket name, but this seems like a hassle and perhaps it's even impossible to change the ticket name.

Thanks for any help.