Soga (蘇我) is derived from the Soga clan and means "Awaken Me". Tojiko (屠自古) could mean "Self-Ancient Carcass". Her name 'Tojiko' is based on Soga no Umako's daughter, Tojiko no Iratsume, who was Prince Shoutoku's consort.
If Tojiko is Tojiko no Iratsume, and Mononobe no Futois Mononobe no Futsuhime, then Tojiko would be Futo's daughter. Tojiko no Iratsume is Soga no Umako's daughter, and Soga no Umako's wife was Mononobe no Futsuhime. However, this is only a speculation because there is no canonical statement saying Tojiko is Tojiko no Iratsume and that Futo is Mononobe no Futsuhime.
Tojiko is the only mid-boss who has at least had a dialog written as this "やってやんよ! (Have at it!)". Which a rather odd way of saying it, as such it has become her catchphrase.