The chord table can be saved to disk as a song file with the File > Save menu command.    Song Files are saved with the .crd file extension.

Song files appear in folders with this icon.  Double clicking on them will launch FastChords and load the song.

When a new song is saved to disk, the title bar of the chord table displays the name of the file. The file name becomes also the name of the song.  It follows that until a song is saved to disk it has no name.

If you have recorded midi performances from a midi capable instrument, then saving songs actually places two files on disk, see Saving / Loading Recorded Midi.