Tokunbo Ajasa-Oluwa, director of the other Catch 22, which trains young people in journalism in Lambeth, south London, said the two organisations had similar client groups and confusion was inevitable.
"They knew we existed before they chose their name, but they didn't consult us," he said. "It's taken less than two weeks for people to start getting the two organisations mixed up.
"If we can't resolve this amicably, I'll be talking to my lawyers. The only satisfactory conclusion is for them to change their name."
A spokesman for the charity - formed by the merger of Rainer and Crime Concern - said it had requested a meeting with Ajasa-Oluwa, but he had so far declined. "Our work is distinct from what his Catch 22 is doing," he said.