Correction of mistakes

Nina_NiaWhat is her last name? I don't know hers/her. (Her is the correct option)

This is correct if you mean that you do not know the person herself.
The first sentence's choice is correct.

PhilipThis is correct if you mean that you do not know the person herself.

But if I want to say that I don't know what her last name is, would it be possible to say; 'I don't know hers'( last name)-without adding the word 'name'?

Yes. Hers (no appostrophe is necessary) is a pronoun that must replace "her name". In the flow of a conversation, it would be very natural. I wasn't sure which you meant, so I gave that other answer.

I should have written it in this way:

Speake.rA: What is her last name?
Speaker. B: I don't know hers.

"I don't know hers" would be correct grammatically, but no-one would say it. In this case, people would say "I don't know her", meaning that since the person is not known to the speaker, the last name is also not known". Maybe you need a better example of your quandary.

Yes, probably my example is not the best. I was wondering if it was correct to remove the word 'last name' and say; I don't know hers, instead of saying I don't know her name.

That is correct, as long as 'name' has been said in the conversation. It's all good now.

Thank you very much, Philip. Your answers are always very helpful.