Someone introduced himself to us.
After that, when we look back and say what he said, which is right to say?
- What did he say his name is?
- What did he say his name was?
Q.
I think the first one is plausible because his name is always XX, but I'm not sure. Please tell me which is allowed.
Reported speech Yes or no? - NO,
after that, when we look back and say what he said, which is right to say?
This sentence is the crux of the Question "tense in a sub-clause" and it is incorrect and as such the meaning is very unclear when coupled with the 2 questions.
when we look back and say what he said
presuming "when we look back and say what he said" should be "when we look back and report on what he said" Then neither of the two question listed above can be correct. As in both cases the name of "he" has been forgotten. Both the questions ask if someone can remember the name. Correctly written reported speech would look like this.
I asked what his name was and he said his name was Dan (conversation that happened in the past).
Therefore if we take the above presumption to be true and we are using reported speech there are no questions only an unambiguous statement "he said his name was (x)". But here we would have to use his name because we are using reported speech not forgotten speech.
Using the two Questions
After that, when we look back and say what he said, which is right to say?
In this case we would have to correct this sentence to Later when we try to remember what he said. Which would be the correct sentence
- What did he say his name is?
- What did he say his name was?
A. The first answer is incorrect because of the context and the second answer is both unambiguous and correct because of the context and tense of the question. Why because we are asking what he stated his name was at that moment in time (The Past). Because in this specific case we are not asking what his name was/is. We are asking what he said.
Incorrect
What did he say his name is?
This is a Question! the speaker cannot remember the name of the person and it may be reasonable to presume that "his name" has not changed, however, in the context of the question, we just simply need to know what his name is not specifically what he said his name was at that time.
the symbol ? used in writing at the end of a phrase or sentence to show that it is a question. Ref CED the symbol ? A Question Mark
Therefore ignoring the misleading reported speech implication. A better question would have been.
Do you remember his name?
Correct
What did he say his name was?
This second answer is an unambiguous question. The lack of context and use of tense gives us no idea about the original conversation, was he introducing himself a few minutes prior or 20 years ago? However I cannot claim that this is not a commonly spoken phrase if used in context and with the correct tense.
Therefore, again, ignoring the misleading reported speech implication. A better question would have been.
Can you remember what he said his name was?
This a defined question with no ambiguity.