I take that to the support, they told me the screen was broken, so they replaced it, but the problem is still there. Now the weird side of the story, that issue is there just after the login screen. If I connect the macbook to an external display, both the internal and exernal starts to be well visible again!
Another strange thing is that I tried to wipe everything, formatting the entire disk and installing a brand new Catalina os (I had Sierra before). All the installation went smootly in the recovery suite (without the external display connected), and the initialization of the os as well. But, after the desktop appeared, the problem was back there.
I tried to reset NVRAM with the P R option cmd combination I tried also to reset the SMC with shift ctrl option combination
Nothing seems to have any effect.
Any idea? Thank you