@Paola412 No, not "at first all good". This wasn'tt okay from the beginning.
3rd party bookings are against Airbnb terms of service. You should never have accepted this booking in the first place. The guest who books has to be one of the guests who stays.
Now you need to contact Airbnb and tell them this person in your home is not the person who booked, that his behavior in your home is unacceptable, and that the person who booked for him doesn't even answer your messages. Telll them this booking needs to be terminated immediately with no penalties to you as the host, as the guest is ignoring all house rules.