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, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
Relating this incident or talking about the person who wronged you is not considered backbiting whether you mentioned his name explicitly or implicitly and whether the listeners know this person or not because Allah, the Exalted, says (what means): {Allah does not like the public mention of evil except by one who has been wronged. And ever is Allah Hearing and Knowing.} [Quran 4:148]
Shaykh Ibn ‘Uthaymeen said:
“The question arises as to whether it is allowed for the person to relieve the grief and pain in his heart by relating the incident to a friend who may not be able to remove the injustice done to him but who may console him. The most likely correct view in this regard is that it is allowed given the general indication of the verse that reads (what means): {Allah does not like the public mention of evil except by one who has been wronged...} This happens a lot; a person may be wronged by being denied his financial rights or the like and relates this to a friend in order to relieve his distress and pain or speak about it with his children, family, or wife, and the like. There is no harm in that because the one who wrongs others has no sanctity as far as the wronged are concerned.”
Hence, you bear no sin for talking about the person who wronged you even if those you talk to know that person.
Allah knows best.