Is it possible to merge two playlists into a third under a new name?
Yes. In the PC/Mac program, just make a new playlist from the File menu and then drag-and-drop the old playlists there.
In the iPhone app, go to Library > Playlist > New Playlist… . Name the playlist and click the “Add Music” plus sign. From there, select Playlists and then choose one of the playlists you want to add. There’s a plus sign for each song and one at the top of the list that will select all the songs in that list to add to your new list. Repeat the process with the second playlist.