USCIS considers the birth certificate name to be the official legal name (unless there is a name change document overriding it), so they took what was on the birth certificate and will place it on the citizenship certificate.
Originally Posted by IT75
On Aug 13 when you go to collect the certificate you will have the opportunity to look at the certificate and comment on any errors. So if you see the patronymic on the certificate you can explain that it's not really a middle name and it's not her green card or any other records and should not be on the certificate (don't forget to look for other errors also!). If they're convinced, problem solved. If they disagree, then she'll be stuck with that on the certificate unless she does a legal name change in a separate court process.
PD: Jan 2003 (EB3 rest of world)
I-485 Approved: July 2007
I am a layman, not a lawyer. What I write here is not official or professional legal advice. In addition, my answers on this forum are specific to the scenarios discussed in each thread and should not be generalized to other situations.