I had exactly this problem.
How it arose was because my undergrad transcript carries my maiden name for middle (since I got married between my Junior and Senior years); to keep the stuff straight when doing LSAC paperwork, I just put in the H from my maiden name.
But I've been using my actual middle name for my legal initial since coming to Colorado. So my driver's license AND my passport AND my city rec center card AND every other legal document for the last 12 years has A for the middle initial.
And of course I didn't notice the discrepancy until the morning of the test. I ran to the bank, got out my passport out of the safe-deposit box, hoping it would have my maiden name somewhere on it, but no such luck.
I was near tears. (And then add the parking fiasco at the test site). What a mess.
But there was nothing I could do about it then. Let's just say it didn't help the pre-test anxiety any.
So I decided to just get in line with the other test takers, plop my drivers licence down with my LSAC ticket, put my thumb on the paper and act like there was no big deal.
The lady glanced at the licence and ticket, glanced at me to see if I was the same person as in the license picture, chopped the print and waved me on. 5 seconds, tops.
The middle initial never even came up.
However, since you've got a week to do something about it, and you sure as sunrise don't want to be sweating this all week, I'd suggest you call LSAC first thing tomorrow morning, get it changed, and reprint your ticket.