Please imagine Evil Grandpa Dooku who keeps trying to get Obi-Wan to join him but ultimately fails each time getting so frustrated that his backup plan is naming Obi-Wan his heir as Count of Serenno. There are many reasons for his mad scheme of varying plausibility, including:
A. He knows Obi-Wan will actually do what's best for the planet instead of leaving it to the idiot government in charge to deal with
B. He is making a dramatic Statement about not being able to escape the lineage you come from even in death
C. He is aware of the non-zero chance of being betrayed by Sidious, so he makes it that upon Dooku's death the New Count of Serenno and leader of the CIS is given all of his Very Important Documents Describing the Sith Lord Immediately
D. No matter how distant or cruel he may be, Dooku is after all part of the disaster lineage and is not above fucking with his grand-padawan from beyond the grave solely because the idea amuses him.
Anyway long story short Obi-Wan has a Very Interesting Time after Anakin kills Dooku aboard the Invisible Hand, starting with being declared the new leader of the CIS. It snowballs from there.