485 RFE, ask xiaobaitu, others, thanks in advance

My daughter's name was AAA BBB in China. We gave her a English name CCC in New Zealand. When she became New Zealand citizen, her full name became CCC AAA BBB. Her original given name became middle name. We do not have any legal document for her name change.

Now the immigration ask to documentary evidence of legal name change from AAA BBB as shown on her birth certificate to CCC BBB.

Any suggestion, idea is highly appreciated!!!!