Is mentioning some narrators with what they dislike considered backbiting?

Question:
Some hadith narrators, like Ibn 'Ulayyah, say: "Whoever calls me Ibn 'Ulayyah has backbitten me?"

Answer:
However, if it is known only by that, there is no harm, such as saying "the one-eyed" or "the blind" for the purpose of identification. It is not intended as backbiting. If he says, "This is a matter of identification," that is why scholars have criticized weak narrators and those who are criticized, if there is a benefit in criticizing them. As some of them summarized in these two verses:
The sin is not backbiting in six cases:
For the one complaining of injustice, the one identifying, and the one warning,
And the one exposing open sinfulness, the one seeking a ruling, and the one
Who seeks assistance in removing a wrong.
Because backbiting is needed for the sake of a legitimate religious benefit.
Q: Well, al-Nawawi, O Shaykh, says: "I do not absolve anyone who calls me or titles me 'Muhayy al-Din.' Should he be avoided?"
The Shaykh: I do not know, by Allah, about the authenticity of this from al-Nawawi, but this is not backbiting; this is a legitimate benefit.