While you are determining who they are, do not let them take control of the conversation, tell them to wait until you are satisfied with the information they are giving you.
Ask confirmation questions like how do they spell their name, and give me your contact phone number, or even e-mail address.
Note: If they have given you a business card, keep it. Photograph any identity cards.
Although this information will be useful, what you are actually doing is asserting your status and dominance over the situation. You are making them wait and putting them on the defensive.
This can be very unnerving for them, and can seriously hinder their confidence.
Do NOT Let Them Talk