Dilemma regarding mother's name on Birth certificate

[siddiqui123]

My wife has an Indian passport with both her names in given name field and has her surname blank. Due to this, Her US green card has her both her names (ex, john doe) in the last name as last cannot be blank and has no name given in the first name field. In her hospital records, she has both names in first name and LNU as last name. In her own birth certificate there is no distinction between first name or last name, it's just written together. 

We just had a baby girl and while applying for the baby's birth certificate it asks mother's birth name and current name. I am not sure whether to match/use her green card or passport or the hospital or the desired state name below.

Our desired state/end goal is to use one of her names in the first name and another in the last name when she applies for naturalization/citizenship but need advice what to do for my daughter's birth certificate.

Edited July 17 by siddiqui123

[pontevecchio]

• Married couples can choose any surname for their children – the surname does not have to be that of either parent.
• So choose appropriately. Your wife can change at the time of naturalization.

[Attorney_22]

You can also have your wife file a formal name change, rather than wait for the naturalization process.