Grammar narration

Question

What is the perfect answer of this question ?

Direct: He said to me "what is your name"?

Indirect: He asked me what my name is.

This indirect speech is correct or wrong. Please help me providing the answer.

Answer 1

There are a number of changes or transpositions you must make to turn direct discourse (a direct quote) into indirect discourse (a report of a quote). I'll use the the following example, in which you're waiting to hear a lecture in an auditorium on March 1st.

Direct: A man asks

"Can₁ you₂ tell me₂ who is₂ speaking now₃ at this₄ lecture here₄ today₃?"

At home, the next day, March 2nd, you want to report the question:

Indirect: A man asked whether

I₂ could₁ tell him₂ who was₁ speaking then₃ at that₄ lecture there₄ yesterday₃.

1. Tense: You received the question in the present, so the man used present tense can and is. The next day, that time of asking is in the past, so the verb forms change to indicate past with could and was.
2. Person: The man was talking to you about himself, so he used the second person pronoun you to address you and the first person pronoun me to talk about himself. But in a report you have to keep clear who was talking to whom. Thus when you talk about yourself, you need to transpose to the first person I, and when you talk about the man, you need to transpose to the third person him.
3. Time: When you were asked the question on March 1st the time was now, but the day of the report, now would refer to March 2nd. So you have to say then. Similarly, when the man asked the question today referred to March 1st, but at the time of the report today refers to March 2nd. To keep the date straight in the report, you have to say yesterday to report about March 1st.
4. Proximity: At the time of the question, this and here refer to something close by in time and place. Now that you're not near the auditorium and it's the next day, you have to indicate remoteness by using that and there, respectively.
5. Sentence structure: For an interrogative clause (a question), the auxiliary verb precedes the subject (Can you). For a declarative clause (a statement) like the report, the order must be reversed (I could).

Let's look at your example:

Direct: He said to me "what is your name?"
Indirect: He asked me what my name is.

The sentence structure changes from interrogative (is ... name?) to declarative (name is). And the person changes from second (your) for the person addressed to first (my). But what about the present tense is? Shouldn't it be transposed to the past:

Indirect: He asked me what my name was.

That would be acceptable but not mandatory because the present tense may be used to describe events that obtained in the past and don't change. The canonical example is

The earth revolves around the sun.

This is called the stative present. Since the stative present refers to past time (unchanging) events, it's not necessary to do the transposition.