Actually, the name "Judo" was already in use. Some representatives of the Kodokan, in the West, at least,actually were making an effort to distinguish Judo (a modern, scientific, civilized art worthy of a progressive 20th century nation like Japan) from Jujutsu (a primitive, thuggish vestige of the medieval age)*.
*(Adjectives in parentheses indicate the ideas presented by these Kodokan evangelists, not my own views.)
I'll bow to your knowledge on it but from my understanding was that the name didn't formally change to judo until 1925. Even then, it was still referred to as jiu-jutsu in Japan for awhile and the name change just never crossed the ocean/took hold in Brazil. I think it was Helio Gracie that said that he never even heard the word judo until much later.