Wonder what the point of disagreement would be. Sakana perhaps wants Sayu to debut with a new identity in Phase? or wants to get ownership of Sayu model? which very understandable Sayu no way in hell is going to relinquish, considering are the money she put on the same. When Fuura Yuri left and had to ditch her identity that she had even before joining Phase, I do admit was one of the few moments I watched the company with a sour face. Sakana is still a CEO after all, huh? I was surprised that she would not be allowed to leave with the identity she built up from before joining them.
Probably that's why the new invaders debuted with original identities and names, so it doesn't look like that they “stole” the previous identity of a vtuber in case she leaves. Which means me think Sakana would want something similar to Sayu, and considering the strong brand the girl has been making as "Sayu" it would also be understandable why she would be reticent to ditch it.
She wants to join a corpo as Sayu.
But...
She really should consider if all of this effort to join a corpo is worth it.