I did have a copy of my birth certificate but the IO did not look at it. She did look at my passport where the patronimic was present, in Russian but not in English.
The patronimic was also written on the bottom portion of my green card (where there was something like machine readable code). However, in the main "name" field of my green card only my last and first names were shown.
A few years before submitting N-400 I applied for a reentry permit. Although I only listed my first and last name on the application, the reentry permit arrived with my patronimic (as -vich) in the "middle name" field. Apparently whomever was processing the I-131 application noticed that in the copy of my Russian passport the patronimic was present; they transliterated it into English and wrote it down as my middle name (although I certainly did not ask for it). Apparently at the time USCIS was on some kind of a campaign to try to give every applicant a middle name - I think they got over it now. I suspect that after that episode with the reentry permit my patronomic was listed in my A-file as my middle name. The IO did not read Russian but she told me that she was aware of the patronimic usage in Russia and the former Soviet states and that she knew that in Russian the patronimic was considered a part of the legal name.
In any case, what the IO did in my case was probably the safest solution. She processed a name change request which allowed me to officially drop the patronimic, and I did not even have to change any of my U.S. documents (driver's license, credit cards, etc), since I never used the patronimic there.