The Honest Man is a nickname; a nom de guerre; it denotes a reputation, a promise, a threat. When an associate of the Honest Man gives you their word, or an ultimatum, you are certain they will not back down. Because if the Honest Man said it, it will be done.
There are many, many criminals in Temma. Not all of them work for Honest Man; in fact, few do so directly. But the large organizations, the families, the gangs, the Secret Societies of Crime, all of those eventually pay homage to the one person by whose graces they are allowed to operate. He keeps the City Guard off their backs. He pries open the doors to the Hall of Justice. He makes the carriages run on time. On their time.