The Hôzôinryû as it is still practiced today stands in the tradition of the secular line of the Hôzôinryû Takadaha which is named after its founder Takada Matabê Yoshitsugu. As Hôzôin Kakuzenbô Inei was the founder of the Hôzôinryû he is of course listed as the first generation of the secular line as well.
The monastarial line:
Hôzôin Kakuzenbô Inei
Hôzôin Zeneibô Inshun
Hôzôin Kakushunbô Insei
Hôzôin Kakuzanbô Inpû
Hôzôin Jôshikibô* Inken
The secular line:
Hôzôin Kakuzenbô Inei (founder of the Hôzôinryû)
Nakamura Ichiemon Naomasa (founder of the Nakamuraha)
Takada Matabê Yoshitsugu (founder of the Takadaha)
As in most koryû (old schools) the line of head masters from the current sôke Kagita Chûbê back to Hôzôin Kakuzenbô Inei who founded the school is well documented.
About the life and doings of the founder of the school on the other hand only relatively litte is known for sure. And the little information that you can find often is contradictory or belongs to the realm of legends.