No, but the moons are connected in the sense that they are like portal points for the Story Eater to traverse through. So since the Story Eater started in Songerein, Songerein's moon would be the "point of origin" in that context.

As for why the moon, moons have always been symbolic both for dreams and source of many folklore and stories, so the Story Eater can feed off both themes and remain true to its original nature, which is being able to travel into different stories and destroy them.