Neither one is correct. It should be: "Have you ever heard of my name?" or, "Have you ever heard my name?" But, if someone is answering back, then they would say: "No, I have never heard of your name." or, "I have never heard your name".

I think the second is right.Because word groups catch on "hear of"and sentences catch on "hear'. Sorry,I am wrong.

The correct sentence should'Have you never heard of my name?'hear of =hear about

The first one is ok, the second should be 'have you never heard of me' or 'have you never heard my name' We never say I have heard of your name. We say I have heard of him/her.