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Explanation: As a complement of the two answers above:
I've heard "Mi nombre es..." mostly in Spain
"Me llamo..." is the most common way of saying it in Mexico and I guess it must be the same for all Latin America.
"Soy...." is a good expression, and I think it can also be used when you are writing; from my point of view this expression sounds somewhat more formal than the other two, but the difference is actually very very very slight.