How to prove mother-child relationship for baby passport if mother's name on birth certificate is different from current legal name?

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My wife's current legal name is SARAH SMITH. On my child's birth certificate, the line for noting the mother says Mother's Name Prior to First Marriage
which shows her name as DONGMEI HUANG.
My wife changed her name legally to SARAH SMITH during her citizenship naturalization process.
When we apply for our child's passport, how do we prove mother-child relationship?
Thanks @Traveller for your comment.
I found USCIS Form N-662 (Petition for Name Change) which shows the old name changing to the new name.
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What can be used as proof of relationship?
Proof of relationship is required, such as a birth certificate or marriage certificate.How can I prove parental relationship in India?
Relationship certificate is a legal document required to prove relationship between parents and their children. This legal paper is required though the children have made their respective citizenship. Supporting documents to be uploaded: Aadhaar Card.How do you prove parent child Relationship Canada?
Sponsors normally need a birth certificate as proof of the relationship with their parents. You should apply for a certified copy of your birth certificate if you don't have one.How do I remove a non biological father from birth certificate in South Africa?
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