For whom is Istikharah permissible? Is it permissible to do Istikharah for an unknown person who is very far away from us in any part of this world?
The person doing Istikharah do not know the name of the person for whom he does Istikharah, but seeks his name, and then seek guidance whether he has been bewitched?
This is described on a TV program "Istikharah Relief From Problems." Is this kind of Istikharah permissible in Islam?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

The Istikhariah that was taught by the Prophet (Sallallahu Alaihi wa Sallam) to his companions is as reported by Jabir Ibn Abdullah (Radiya Allahu Anhu) in Sahih al-Bukhari that the Prophet (Sallallahu Alaihi wa Sallam) "Taught us how to make Istikharah in all (our) affairs, just as he taught us various surahs of the Qur'an. He told us, 'If anyone of you considers doing something he should offer a two-rak'at prayer other than the obligatory prayers, and then say (after the prayer). (O Allah ! I ask guidance from Your knowledge, and Power from Your Might and I ask for Your great blessings. You are capable and I am not. You know and I do not and You know the unseen. O Allah! If You know that this thing is good for my din and my subsistence and for my Hereafter - (or say, If it is better for my present and later needs) - then ordain it for me and make it easy for me to obtain, and then bless me in it. If You know that this thing is harmful to me in my Din and subsistence and in the Hereafter--(or say, If it is worse for my present and later needs)--then keep it away from me, and keep me away from it. And ordain for me whatever is good for me, and make me satisfy."

Making Istikarah is allowed only to the one who is in need of Istikharah. It is not allowed to be done on behalf of another person if he is able, to carry it out since no one is supposed to perform the prayer on behalf of someone else.

Muslim scholars have agreed upon that neither obligatory prayer nor Sunan (optional prayers) could be performed on behalf of others. Imam Abdul Barr Reported this Ijma'h (consensus) in his book al-Isdizkar.

However, making Du'a for one's brother is allowed. So, one may make Du'a to Allah for his brother to be guided to what is beneficial for him.  Du'a of a Muslim to his absent brother is responded to as mentioned in Sahih Muslim that the Prophet (Sallallahu Alaihi wa Sallam) said: "If a Muslim supplicates Allah for his Muslim brother, Allah answers his absent supplications.  An angel says to him "Ameen," and he also says: 'May it be for you as well." [Muslim]

As for making Istikharah to find out whether someone was bewitched or not by asking his name, his parents names, etc. is among the features of magicians and tricksters, as mentioned by Sheikh Waheed Abdul Salaam Bali in his book on this subject.

Allah knows best.