Is there any Islamic method to find the name of the person who did black magic to you

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Knowing the person who did magic is either by his confession that he was the one who did magic, or by the testimony of trustworthy witnesses that they saw him while he was doing magic.

However, without confession or evidence, one should absolutely beware of accusing someone of this dangerous accusation.

Moreover, treating magic, if we presume that it exists, does not necessitate knowing who did it. Rather, whoever performs Ruqyah on himself with the Islamic Ruqyah and confirmed supplications from the Prophet and seeks help from Allah and was sincere to Him, then Allah will spare him of this disease as Allah Says (what means): {And We send down of the Quran that which is healing and mercy for the believers.} [Quran 17:82]

For more benefit on Ruqyah, please refer to Fataawa 4310, 31469, 13277, 170973, and 117025.

Allah Knows best.