Is it necessary to have my full name (including middle name) on my student pilot license?
Alright so here is the outcome: 

I called FSDO, spoke with a real nice guy who told me to give him a call if I couldn't handle this online.

Called a zillion bureaucracies, all telling me to call someone else.

Called the nice guy at FSDO, set up an appointment for a name correction not a name change. Went to the appointment and was in and out in under an hour.

If you're having the same issue, I would recommend bringing every official identification you've got: passport, birth certificate, drivers license, etc.

Tl;DR call FSDO and tell them you need a name correction. NOT a name change. Can't stress that enough.