The answer is, “When you bring the people out of Egypt and serve God on this mountain” – i.e. your identity will be shown in your actions. You are not what you claim to be but what you do.
The Ishbitzer Rebbe (R. Mordechai Yosef of Isbitzes, early 19th cent.) used to say that who I am is not merely a question of name, age, address or occupation. I am revealed in my relationship with my soul and in the way I relate to others. If I do not deal with other people in a moral and ethical way there is something wrong with my identity.
Hence Moses was told to prove himself in terms of others (bringing Israel out of Egypt) and his own soul (worshipping God on the mountain).