I'll try to describe some situations in which I would use the different expressions: I would use "Mein Name ist..." in a formal situation, for example if I had to introduce myself to an audience or if I talk to an office assistant at a registration desk to see a lawyer or a doctor. I use it also if I introduce myself to somebody unknown on the telephone. " Ich heiße ..." is less formal. I would use it to introduce myself to a small group of people I don't know yet, but maybe get to know better, for example meeting new colleagues at work. "Ich bin ..." is the least formal way to introduce oneself and usually only refers to your first name. I use it if I expect to say "du" to the other, for example with children or friends of friends. I also use it if I expect my counterpart to hardly understand or if I want to imply that I'm friendly, caring, a likeable person, e.g. with little children or persons in need of care or help. But often enough you just say your name without any introductory " Mein Name ist" or "Ich heiße". I hope this was kind of helpful.

Hi. I do not agree with Andrea’s classifications by politeness… In fact I’ve heard that „Mein Name ist […]“ is not even standard German and came from lousy Englisch movie dubbings. I think „Ich heiße […]“ and „Ich bin […]“ is both just normal tongue. Please correct me here if I’m wrong here.

there are more ways to introduce yourself. all of yours are good, and it doesnt really matter which one you choose. its just diffrent if you want to talk in a formal way.