Well I would actually have it the other way round. You would hear "Ich bin" much more often than "Ich heiße" in day to day language. It is much more common to shake hands and say "Ich bin". Though both are correct, the form "Ich heiße" sounds much more textbook style and stiff. When meeting friends you would rather say "Ich bin". In a much more formal setting, like meeting a business partner you would just say your name when shaking hands leaving out any introductory forms.

German is not my first language, but I just asked my step father who grew up there and he said that "Ich heiße Carolina" would be more accurate. "Ich bin die Carolina" would still technically work, but it is less commonly used. I have often had the same question. Hopefully, this helps.