indirect speech

[chrysanthemum]

"What is your name?
The teacher asked what my name was?
I know that when the reporting verb is in the past we should change the tense of the verb in quotaion marks. But can this sentence be correct?
The teacher asked what my name is? I mean without the changing of the tense?

In my book there is a sentence: He asked, "Where do you work now?"
He asked where she worked now. Why didn't the writer change now to then?
Thanks

[Calis]

Although it makes sense to change it to "what my name is," because your name is always going to be the same, it all has to be in the past tense.
"The teacher asked me what my name was."

It is "he asked where she worked now," because he asked her in the past, but where she works is current. Then would mean he asked her where she worked in some time in the past, either at the time the conversation went on or a time before that.

[Not a teacher]

[spongie]

I'm not a teacher.

"What is your name?"
The teacher asked what my name was. You shouldn't have put question mark at the end of this sentence.
I know that when the reporting verb is in the past we should change the tense of the verb in quotation marks. But can this sentence be correct?
The teacher asked what my name is. I mean without the changing of the tense. I think that this sentence is also correct.

In my book there is a sentence: He asked, "Where do you work now?"
He asked where she worked now. Why didn't the writer change now to then? I believe the writer made a mistake. It should be "then" instead of "now".
Thanks