What is the difference between "שמי" and "אני" when stating ones name?
Which is preferred? Depending on my resource, I am taught either or, but never both.

Question

Answer

אני - I Am (informal, used more often)
שמי - My name is (formal, archaic)

אני צביקה = I am Tzvika
אני עייף = I am tired
שמי צביקה = My name is Tzvika
שמי עייף = nope, doesn't work.

Answer

The most common way of telling your name is: קוראים לי, literaly means "[they] call me", but it's a fixed expression used to tell one's name.
e.g. קוראים לי רמי. (My name is Ramy)

Answer

Shemi (my name is)