Here it would be appropriate for you to say my name is and your name or I'm and your name. If you don't know this person's name you could respond with, What's yours?
What is your name?
Here the person is asking about your occupation. What you do for a living or what do you do with most of your time. You can respond by saying where you work and what you do at that workplace, or you can respond by saying you're a student or are in school if that is the case.
What do you do?
What do you do with yourself?
The person is asking about what activities you find enjoyable. Do you like playing soccer, watching movies or playing computer games.
What do you like doing?
What hobbies do you have?
The person could be asking where you are from in terms of country, city, or area or they could be asking which company you work for, depending on the situation.
Where are you from?