Is mentioning people unknown to the listener considered backbiting, and am I sinful if I denounce backbiting by saying, "May Allah bless you, I am not prepared to give away my good deeds," yet the backbiter continues with their backbiting?

Forbidden backbiting concerns a known person. And whoever verbally denounces backbiting has fulfilled their duty and cleared their conscience, based on the Prophet's (peace be upon him) saying: "And whoever strives against them with his tongue is a believer," and his saying: "If he is unable, then with his tongue."

There is no blame on him if he completes [listens to] the backbiter, but he must leave the gathering if he can, otherwise [disapprove] with his heart.

Al-Nawawi said: It is obligatory upon anyone who hears backbiting to forbid it if he does not fear harm. Otherwise, disapproval with the heart and leaving the gathering is obligatory if possible. If he is compelled to remain in it and is unable to forbid it, or his forbidding is not accepted, then listening and paying attention become forbidden to him. His way [to deal with it] is to remember Allah or think about something else, and hearing it will not harm him then.