Can people change the name of a collaborative playlist?

If you're on the desktop version of Spotify, look to the panel on the left. You'll see "New Playlist" for, yup, new playlists. If you're looking for existing playlists, scroll below "Your Library."

Right-click on the playlist and select "Collaborative Playlist." A circle icon will appear to indicate that it is indeed collaborative.

Then look for those three horizontal dots to share your playlists via any social or messaging app listed. Or you can share via a link [which is your only option if you're using the web player version of Spotify].