Student or Learner
He asked me what my name is and where I came from.
REMINDER: NOT A TEACHER
(1) Tom speaks to Martha on Monday: What is your name and where do you come from?
(2) Mona speaks to Martha on Tuesday: What did Tom ask you yesterday?
Martha: Oh, he asked me what my name was and where I came from.
(3) I believe that the answer in (2) would be in accordance with the rules.
(4) But some native speakers might be more comfortable in saying:
Oh, he asked me what my name is and where I come from. And I told him that it
was none of his business!