Will my ticket bought through cheap tickets work at a Chinese airport?

My girlfriend is flying from Beijing to the US. I bought her a ticket from cheaptickets.com. The e-ticket would definitely work in America but I'm worried if it will work at her Chinese airport. From what I can tell, the traveler information provided is her full name and airline ticket number. The cheap tickets booking number and airline record locator is also on it.

I'm worried this might not be enough information. I refunded her last ticket because the first and last name were reversed and the airline told her she might be denied boarding. Thus, I bought her this new ticket with a new airline. Although her first and last name were definitely entered in correctly in their system, on the e-ticket it lists her name as Z***** L**, with her last name as L**. This is correct because US convention is to write first name first and last name second. However, the convention is opposite in China and I worry the airline may deny her boarding because of this.

Are my worries unfounded?

EDIT: I know the it is entered in the system correctly because when looking up her records I am asked to enter in her last name and I use L**, which is correct. What I am worried about his how it is written on the ticket and whether this will affect anything.