On the 4G iPod it does make and save the playlists, but you can't rename them (AFAIK) on the iPod. They are just called "On-The-Go N" where N is an incrementing number. They are saved and copied to iTunes tho. My iPhone has inherited 15 of them.
http://www.everymac.com/systems/appl...od_4thgen.html
Not at all the same as the next iPhone that was lost/stolen recently.