Omission of a Middle Name on EAD and SSN

I received my EAD a while ago and now have my Social Security Number. However, when I got my EAD, one of my middle name was missing (I have 4 names). For example (not using my real name): My name is Carol Sydney Claire Smith. On the EAD, it only says Carol Sydney Smith. Therefore, when I got my SSN, it only shows Carol Sydney Smith

I just finished my Drivers Education class. I heard that when going to the DMV, all documents must match exactly the same. However, on my passport and birth certificate my FULL name is written, Carol Sydney Claire Smith. When the DMV looks at this, will there be problem? Will I still get my license?

I don't see any reason why not. As long as both documents indicate Carol Smith and one doesn't say Carol while the other says Carrie, and they both say Smith instead of one saying Smith-Jones, you should be fine.

Alright. I'm going to the DMV on monday. Hopefully everything goes well.