Ame-no-Habakiri is the one Susaoo used to kill Yamata no Orochi
There are multiple swords of the Totsuka-no-Tsurugi with each having their own legend.
Ame-no-Habakiri is the one that is known to slay Orochi and became enshrined as the Shintai of Isonokiami Shrine
The new beast tribe called Kojin are the Shinto religion beast tribe just like how Ame-no-Habakiri is enshrined in a Shinto Shrine which is Isonokiami Shrine.
Ama-no-marakumo-Tsurugi was the sword found inside Yamata no orochi after Susaoo killed it.