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.

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)

Shemi (my name is)