In China you refer to a person's family name first IE. Smith Tony - so it's not surprising that you note the order is reversed.

Anyway well done for battling the website and getting independent confirmation the ticket exists. Unlike most OTAs, trip.com is actually a decent operation, they answer the phone and are broadly clueful and provide a competent service, do have team members who speak English, do don't be shy to speak to them if you need to.