In order to suggest the name of a professor who can follow you in your thesis, you can forward the abstract of the thesis, or the idea of what you would like to develop, through the "send an email" channel http://www.design.polimi.it/en/askforassistance/ under "Conclusion of the studies".
Then, the material is submitted to the Coordinator of his course of study for advice on the supervisor.
Alternatively, if you have not yet set a thesis topic / project, you can consult the Thesis Bulletin Board http://www.design.polimi.it/en/studying-design/bacheca-tesi/ where you can find the theses proposed by some professors, in relation to the course of study.
You can find the composition of your Operational Commission (CO in Italian) from your online services in the application for enrollment to the graduation exam.
The day before the discussion you can check the time of the discussion from your online services in the application for enrollment to the graduation exam.