How do I change my iPod's name?
If it is running iOS 5, you should be able to change it in Settings>General>About>Name:


If it is running anything less than iOS 5 (or is just a click wheel iPod) you'll need to plug it into your computer and change it from iTunes. Click on the name in the sidebar and change it:

If this still doesn't work (and doesn't show up on the iPod), try restoring (in iTunes) it, or restarting it (hold down the center button and the menu button for 10 seconds)