Lumiya, then Caedus. Lumiya was trained by Vader directly making her the only candidate to continue the Rule of Two line since Vader and Sidious were the last Rule of Two Sith Lords. Darth Caedus next because she convinced him using Sith teachings and Caedus even made a sacrifice to become a Sith before he chose his Sith name.
However technically Lumiya isn’t a real Rule of Two and is more like a Dark Jedi with Sith Lord levels of Power and skill. Because she never went through the rituals of being hit with Sith lightning and making a sacrifice to become a Sith.
Darth Krayt I remember actually offended all the Sith Spirits he spoke to; being Darth Bane, Andeddu, Nihilus. With Darth Bane directing saying Krayt and his order were not “Real” Sith. And all other spirits refusing to help him. So Krayt’s definitely not the successor. Although I think him and his order were actually quite cool.