I have two middle names. On my social security card, only my first middle initial is listed. The second middle name is completely omitted. I'm not sure if other people have their full middle name on their cards, but I always supposed that the problem with mine was that my first name is also unusually long and they ran out of space or something. At any rate, I actually go by an abbreviated version of my second middle name (NOW, that wasn't the original intention of my parents) and it hasn't caused me any problems. When I need to fill out forms I will put all four names down. If there isn't room I just put my two middle initials down.
I will say that things seem to be changing on that front, though. Both of my girls also have two middle names. On the oldest one's SS card only her first middle name (in it's entirety) is listed. The second is left off. Whereas with my youngest, her full name (no abbreviations) is listed on her card. I still fill out forms like usual. Full name when asked for, and just the initials when there isn't room or the form specifically asks for the middle initial.
I'm me. In love with this guy. We're bringing up two girls: Big A (8) and Little A (3)