The first member to bear the name Ransome, the Reverend Josiah Jesse "J.J." Ransome-Kuti, adopted it in honour of the Anglican missionary who had first converted his family to Christianity.

[1] He followed his father Likoye Kuti — an Egba griot — into the musical vocation, and wrote a series of popular hymns in the Yoruba language while serving as an Anglican cleric.

The descendants of J.J.'s son, the Reverend Israel Oludotun Ransome-Kuti, and Chief Funmilayo Ransome-Kuti include a health minister (who had also served as a university professor), a political activist (who would himself later be adopted as an Amnesty International prisoner of conscience), and six further musicians (including one who founded and led a political party and three Grammy Award nominees).

The Ransome-Kutis have been known to form marital unions with other families of the Yoruba elite: the branch descended from Chief Funmilayo Ransome-Kuti is a sept of the aristocratic Jibolu-Taiwo family of Egbaland by virtue of its descent from her, while the one descended from the Reverend Samuel Ayodele Soyinka, the husband of Grace Eniola Jenkins-Harrison, is related to the royal family of Isara-Remo through him.

In 2017, in Abeokuta, the house on NEPA Road where the family of Israel and Funmilayo Ransome-Kuti lived was transformed into the Ransome-Kuti Museum, dedicated to the history of the family.