In the track header (editor window, left pane) is a button labelled p (for "Playlist"). If you click on this button, Ardour displays the following menu:

(Local Playlists)
Shows all of the playlists associated with this track, and indicates the currently selected playlist
Rename
Displays a dialog to rename the current playlist
New
Creates a new empty playlist, and the track switches to the new playlist
New Copy
Creates a new playlist that is a copy of the current playlist; the track switches to the new playlist
Clear Current
Removes all regions from the current playlist
Select From All
Displays a playlist browser to manually choose which playlist this track should use. (You can even select playlists from other tracks here)

Renaming Playlists

Playlists are created with the name of the track of which they are associated, plus a version number. So, the first playlist for a track called "Cowbell" will be called Cowbell.1. This name will be used to define the names of any regions added to the playlist by recording. You can change the name at any time, to anything you want. Ardour does not require that your playlist names are all unique, but it will make your life easier if they are. Suggested examples of user-assigned names for a playlist might include Lead Guitar, 2nd take, vocals (quiet), and downbeat cuica. Notice how these might be different from the associated track names, which for these examples might be Lead Guitar, Vocals and Cuica. The playlist name provides more information because it is about a specific version of the material that may (or may not) end up in the final version of the track.

If you are going to rename your playlists, do so before recording new material to them.

It appears that recorded regions are not named after the playlist, but after the track.

Sharing Playlists

It is entirely possible to share playlists between tracks. The only slightly unusual thing you may notice when sharing is that edits to the playlist made in one track will magically appear in the other. If you think about this for a moment, its an obvious consequence of sharing. One application of this attribute is parallel processing, described below.

You might not want this kind of behaviour, even though you still want two tracks to use the same (or substantially the same) playlist. To accomplish this, select the chosen playlist in the second track, and then use New Copy to generate an independent copy of it for that track. You can then edit this playlist without affecting the original.