I also think that wasn't Shaggydog and that Rickon and Osha are there because of a plan, not because yet another northern house turns out to be traitorous morons.
I think Dawn wasn't mentioned because they want to forego confusion about too many important swords. There's already Ice (now Oathkeeper and Widow's Wail), Needle, Longclaw, and Lightbringer. No need to bring even more swords into it in the show.