To ask What is your name? say Как Вас зову́т? (formal, polite) or Как тебя́ зову́т? (informal).
The phrase Как Вас зову́т? is used in the same type of relations as здра́вствуйте.
The version Как тебя́ зову́т? is used for the same type of relations as both здра́вствуй and приве́т.
Literally both questions translate into How do they call you?.
To say My name is... use Меня́ зову́т…. Literally it translates into They call me… .
