They explained it earlier during the beta I believe, but I am taking it as a title. Cricket being the title you are given while you are just starting out. Jyan being the next step up, and Jyansei being the one after that. Just think of it as a title that people call you when they don't know your name. Same way (I guess) with why Mushin is called Mushin and not his actual name.
There is a lot of eastern culture wrapped into this game. You either need to accept it and adapt to new terminology, or find another game. This game is very rich in lore, and even as someone who doesn't