One further China Southern complication..it just doesn't end!

One of us has received a new passport and so I emailed them to update the password details. They asked for a photo of both passports - fine. Their response was that they noticed the middle name was missing from the ticket but said they can only do one free change, either the passport number/exp date or name. Problem is, I excluded the middle name when buying. 3 of us would need a change to add a middle name, incl one who would need a 'De' added to the surname box (like De Silva). I have never had any kind of issues before flying with just first name/surname but their reply has spooked me.

Should I just leave it as is or somehow try to get them to change it to add the middle names, since it is a Chinese airline and we are going through immigration in China now?