Why does the name of my flash drive change whenever I demount, then remount it?
It has always been the case that changing the case of a USB volume formatted with FAT required some low-level hacking. 

There are instructions to do this in the following link: (a word of warning: I have not tried this and making a mistake with some of these low level commands may wreck your drive, so be careful!)

http://hints.macworld.com/article.php?story=20090506034709445

Also see the thread here for instructions to change the drive icon if you so desire.

http://forums.macrumors.com/showthread.php?t=677658