My question involves name change laws in the State of: New Jersey

My soon-to-be-ex-wife wants to add her last name to the children's middle name, but I see this as a potential child abduction opportunity and here's why:

A Chinese name is typically 3 characters formatted as such: [Father's Family name] + [Given name part 1] + [Given name part 2]

In my Asian-American experience, American born Chinese names are formatted as such:
[English Given Name] + [Chinese Given name part 1] + [Chinese Given name part 2] + [Father's Family name]

As part of our custody settlement, my wife wants to add her family name to the children's middle names so that it would read as such:
[English Given] + [Chinese Given 1] + [Chinese Given 2] + [Mother's Family] + [Father's Family]

My concern with agreeing to this is while the children's identities in English would be protected by the Hague Convention agreement against spousal international abduction, allowing the children to have essentially a full 3-character Chinese name legally included as part of their identities could somehow be misidentified in Chinese-speaking countries as their full legal name alone thereby misidentifying the children as fully hers and unrelated to me, and circumventing or greatly obfuscating the protections of the Hague Convention. My wife currently still maintains citizenship in a couple of those sovereignties, and one of the kids also does have one matching foreign citizenship, so the flight risk is real.

This is a combination divorce law, family law, name change, immigration, and foreign immigration issue so I'm having a hard time finding an answer to this through any single expert.