If you use Mac OS X 10.2.8, you won't be able to rename your iPod shuffle in the Finder. The iPod shuffle drive is formatted using the File Allocation Table (FAT) format. Mac OS X 10.2.8 does not support the renaming of FAT formatted volumes.
If you rename iPod shuffle in iTunes, the name will not change in the Finder.
You can rename your iPod shuffle so the Finder displays the new name if you have access to a Mac with 10.3.4 or later and built-in USB or a Windows-compatible PC that works with iPod shuffle. Check here for system requirements. The renamed iPod shuffle will then work fine with your computer using Mac OS X 10.2.8.
When renaming any FAT-formatted volume (including iPod shuffle) in the Finder, you can't use double-byte characters (including Chinese, Japanese, and Korean). If you try, you'll see this error:
Use only Roman characters to rename the iPod in the Finder. You can use double-byte characters to rename the iPod shuffle in iTunes.