Translation:I don't know that person's name.
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)
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.