RFE for name change that wasn't actually a name change

[EcuatoriAnna 0]

My husband (USC) has filed an I-130 to bring his Ecuadorian mom to the US. He received an RFE that we're not quite sure how to address, and would appreciate any advice. His mom has two last names, so her full name is (altered for privacy, but this is the idea): Julia Maria Gutierrez Rivera. On my husband's birth certificate, her name appears as Julia Maria Gutierrez (without the second last name). On all other documents her name is listed as her full legal name: Julia Maria Gutierrez Rivera. He got an RFE for "Proof of Name Change" and has been asked to show evidence of a name change (birth certificate, marriage cert, divorce decree, etc) to show that Julia Maria Gutierrez and Julia Maria Gutierrez Rivera are the same person. The thing is, she has never changed her name, so there isn't any proof of a name change.

 

Julia did go to get my husband's birth certificate corrected with her full name. The correction consists of a note attached to the birth certificate saying essentially "This registration is rectified in accordance with XYZ laws on X date that the last names of the parents are Morales Castillo (father's two last names), Gutierrez Rivera and not as recorded." The note is signed and has a seal on it. I'm wondering if this is sufficient evidence to address the RFE. We plan to draft up an explanatory letter to go along with the corrected birth certificate, but it's not exactly the evidence they asked for (i.e. it's not evidence of a name change, because her name has never changed), and also the correction isn't exactly crystal clear. That is, it doesn't outright list Julia's full name. It just says the parents' last names are: Morales Castillo, Gutierrez Rivera.

 

Has anyone else had a similar experience? Is there anything else we should do to clear up this situation? There aren't any documents that we're aware of that list Julia's name as "Julia Maria Gutierrez" to show that both names refer to the same person, though it is not uncommon for people in Ecuador to just utilize their first last name in social settings. Any help would be much appreciated!!