Mistake on I-551 on passport stamp, advice?

[acrufox 6]

I entered the USA at the end of October and today I went to the Social Security office to request a SSN. I asked if they could find me in the SAVE system to which she could not. She took another look and found that I was in the system with my middle name placed with my first, no middle name, and my last name.

The woman provided me with a phone number to call Homeland Security who then referred to me make an appointment with my nearest USCIS office to make the correction (123 Miles away, ugh) I have made an appointment concerning this~

Should I just bring my long form birth Certificate and Passport with me as proof of my name? This isn't exactly a typo, and I haven't received my permanent green card yet either, I'd like to avoid paying a filing fee of $365 since I wasn't the one that made this mistake~ What should I expect since this error was spotted only two weeks into entering the US.

Any advice?

Thanks!

Edited November 15, 2016 by acrufox