I don't keep my music in iTunes and I manually manage music and videos. I only use iTunes to transfer songs (i.e. add files/folder) onto my iPod I then delete it from iTunes. I've always done it that way.
Hhhmmm! Now's the time to re-think that method then, especially if you have music on your iPod from sources other than the iTunes Store.
Apart from anything else, if you delete the music from iTunes, then when the iPod requires a Restore, or is stolen or lost, then everything on the iPod will be lost as well. You will have no Library to use to add that music to a new iPod. Not just that, but when you eventually decide to replace that iPod with a newer model, you will then be faced with the problem of how to get the content of the old iPod onto the new one.
Further, if you also delete the music from your computer (you haven't said that you are doing so, but usually the reason why people delete music from iTunes is to save storage space on their computer), then you won't even have the music anywhere on your computer to add back to iTunes.
My advice - which you are perfectly free to ignore - is:
- keep all your digital music in iTunes (it's the back up for your iPod) - and then back that up too, onto something like an external hard drive.
- make the changes in your iTunes Library first - and then use Sync to put those changes onto your iPod.
- at Sync time, any Playlists created on the iPod should be put into your iTunes Library. Once that has happened, you can change the Playlist's name and then use Sync to synchronise that change back to the iPod.
By the way, just so you know, people may tell you to use Apple's iCloud to "back up" your iTunes Library. Personally, I think that's a risky strategy;
- as far as I'm aware, that will not include music ripped from your own CDs (and definitely not if the iTunes Store doesn't have that CD), Podcasts, home videos etc. etc.
- as far as I understand it, if a song (or album) is removed from the iTunes Store (for example, the artist deciding they don't like the financial arrangement with the Store), then their songs may disappear from your account as well. If I'm wrong on this point, I'd like someone to explain it clearly.
So possibly the reason that you are experiencing difficulties with Playlists is:
- Playlists created on an iPod need to transfer to the iTunes Library, then have their name changed and then Synced back to the iPod.
- There is no reason why iTunes should Sync an empty Playlist. There's nothing in it, so what would be the point?