For anyone reading this and that’s confused, towards the beginning of the manga Miyamura and Ishikawa we’re going to call each other their first names but Miyamura just ended up forgetting about it so they never switched. Now, Yanagi is calling Ishikawa his first name and by telling Miyamura that he “won’t take what’s yours,” I think Yanagi is trying to say that he won’t try to get too close to Ishikawa and force Miyamura and Ishikawa’s friendship to suffer.