When you export the setlist in HD500 Edit you can simply overwrite the default yymmdd filename to the desired setlist name. That becomes the saved filename, and hence the setlist name when the saved setlist is restored.
Thanks for the answers.
I think I was wrong - the names are kept when saving a setlist.
There is just a strange behavior when importing a setlist. Then as Name the filename of the imported setlist is shown, but when sending the setlist to the HD500 and closing and reopen the HD Edit the initially given name is displayed.