Translation:I don't know that person's name.
Not even going to lie, thought it was, "I don't run that person's name". Was just like, erm what...?
Please notice that 知りません, or the non-polite form, 知らない, sometimes implies "I don't care!" if you are asked about other people's business.
If someone asks you "Do you know a famous animated drama called 君の名は?" You may answer "知りません" to simply express that you don't know that fact / You had not gotten that piece of information.
But if your friend is looking for his wallet and asks you "Do you have any idea where my wallet is?" Answering "知りません" may imply "I don't know, and it is your business." In this situation, "分かりません/分からない" will be a better response.
In addition, you can use "もう知らない！" to express "I don't care anymore!" (Technically the polite form is もう知りません, but the situation seldom matches)
Why was 知っている used in "あの女の人の名前を知っていますか？" But here it's just 知る? How do I know which one to use?
Here, the phrase is "do NOT know". In the negative case of knowing, I was taught it always uses 知りません and not the negative 知っていません.
Is there any specific semantic reason as to why it would be so? Perhaps that, because we want to express a negation, stating that the one-time action did not take place is enough to ensure that the subject is not in the corresponding continuous state (i.e., if one does not come to know, then one is not in the state of knowing)?
I am just hypothesing a bit, there.
I remember learning this in uni. The logic we were given is that when you know something, you will always know, you can never unknow it unless you have amnesia, while when you do not know something, it does not have to mean you never will.
Ah, so I was close enough! Some fine casuistry for the mind. Thank you. :)
I can't believe i didn't accept "I do not know" instead of "I don't know"
知っていません ("am not knowing") should be OK, but 知ってません is not because ません is a suffix, not a word.