IMHO you should answer "Jestem Anne" lub "Mam na imię Anne". 'Nazywam się' is related to "nazwisko" - surname and should only be used with your surname or both with the surname and first name. And I also think that the most natural way of responding to such a question is just giving your first name: - Jak masz na imię? - Anne. :)

hey:) To be honest it doesn't matter because all forms You put in here are correct:) If somoeone asked "Jak masz na imię?" (What's Your name?), You can answer: 1. Jestem Anne. 2. Nazywam się Anne. 3. Mam na imię Anne (numbers 2 and 3 mean the same thing, the only difference is that when You're using number 2 You can also tell what's Your surname).