I found this to be very interesting and I am compelled to give my own opinion, if I may...

The correct way of introducing your self is, "My name is". Our brains work mysteriously, we are able to determine whether this is a name or a state reference because...

1. Our brains have lists of words in English that are name references.
2. We know that when something sounds weird is probably not a name.

However, there are times that it becomes ambiguous... for example picture someone whose name is Happy and he introduces himself saying, "I am Happy". It's not much of a problem when he writes it because names start with capital letters in a middle of a sentence so at least one can know after analysing that his name is Happy. But speaking it... it sounds really ambiguous hence it is good to say, "My name is".

I hope I helped.

The correct way of introducing your self is, "My name is". Our brains work mysteriously, we are able to determine whether this is a name or a state reference because...

1. Our brains have lists of words in English that are name references.
2. We know that when something sounds weird is probably not a name.

However, there are times that it becomes ambiguous... for example picture someone whose name is Happy and he introduces himself saying, "I am Happy". It's not much of a problem when he writes it because names start with capital letters in a middle of a sentence so at least one can know after analysing that his name is Happy. But speaking it... it sounds really ambiguous hence it is good to say, "My name is".