N-400 Name mix up

[dietSnapple]

I just came back from my N-400 interview in Seattle. As soon as I walked into the Immigration Officers office for my interview, she mentions that she has a few questions about my name. After going back and forth with her for a couple of minutes, I thought that I should let this one go and worry about it later. I didn’t see any point of arguing with her because we both thought we were right. Anyway, here is the situation:
My name as it appears on my birth certificate, passport:
firstName middleName - xx - lastName

These dashes don’t really mean anything in my culture. So I have always used my name as following:
First Name: firstName
Middle Name: middleName xx
Last Name : lastName
This is how it is on everything for me: SSN, driver’s license, my marriage certificate, my wife’s pending I -130.

One my green card name appears (which I never noticed until today):
middleName - xx – lastName, firstName
So therefore my new name now is:
First Name: First Name
Last Name: middleName - xx – lastName

I have passed the interview, and oath is next week. I don’t really care about how my name is written; I am just worried about my wife’s I-130. I was going to upgrade her I-130 from permanent resident to citizens once the oath is complete. How can I fix this name issue, and how do you think it will affect her process.

Thanks in advance for your help.

 

[Bobsmyth]

So they combined your last name as your middle name and your last name. I don't see an issue with updating the I-130 as they will see the alternate spelling of your name on the application.