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Hi. Please help me with this. Let us pretend that someone (a man)received a call asking for his address but the person who called didn't ask, "What is your address?" but rather asked, "Where is your home?." After getting the phone, the person who received the call called his wife to tell her that someone had called him to ask where their home was (is??). Let us also assume that in that part of town it is common for a delivery person to ask for someone's address or where a person lives.

(calling his wife)

Man: I just received a call from someone.

Wife: What did he ask you?

Man: He asked me where our home was (is?).

Could it be the same for the name?

Man: I just received a call from someone.

Wife: What did he ask you?

Man: He asked me what my name was (is?).

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The standard answer is that it's never incorrect to backshift in reported speech.

It's fine to use present tense when the condition is still true.

You wouldn't say, "Caesar asked Brutus where his toga is." ("Brutus! Where's my toga?")

In your examples, you may use either one.
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Thank you for your help.