if I have a playlist, and I copy it to another section (via copy/paste), and then I modify the name of the copy... the name of the original changes too.

This is normal behavior for both Emplode and Jemplode. You're missing the point of how the player is organized. It's designed so that you don't waste space with copies. Each copy is just a link back to the original. FAQ entry here. You want something other than a "copy", which has been discussed elsewhere in this thread.