Assalaamu alaykum, my question is with regards gheebah (backbiting):
A. If I narrate a story for sympathy or with sorrow, but not to belittle, is this considered gheebah if it may shed bad light on someone?
B. Alternatively, if I narrate the same story, but without mentioning names, is this gheebah? Ideally, we would not need to ask, but due to human nature, we sometimes share events. May Allaah reward you for your reply.

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

We have already mentioned the conditions that determine what is Islamically considered gheebah (backbiting) in fatwa 81748, and we highlighted the situations wherein gheebah is permissible therein. Based on that, you would know the ruling on what you asked about and whether or not it is included in gheebah and if there is a concession regarding it. This is with respect to your first question.

The answer to your second question is that if you do not specify the person and the listeners do not know him, without identifying who he is, then there is nothing wrong with relating his story. It was confirmed that the Prophet said, “What is the matter with some people who said such and such...” [Al-Bukhari and Muslim]

Nonetheless, it is known that it is better to avoid this unless there is a benefit in doing so. The Prophet said, “Among the good traits of a Muslim is to avoid that which does not concern him.”

On the other hand, the time of a Muslim is more precious than to be wasted in matters that do not bring any benefit to him in his religion and his worldly matters. Ibn 'Abbaas narrated that the Prophet said, "There are two blessings in which many people incur loss: health and free time." [Al-Bukhari]

There is nothing wrong for a Muslim to get involved in what happens around him, but he should judge this according to the conditions of the sharee'ah. For instance, he should not relate everything that he hears, and he should not talk too much about what is not beneficial. Allaah says (what means): {And do not pursue that of which you have no knowledge. Indeed, the hearing, the sight and the heart - about all those [one] will be questioned.} [Quran 17:36]

Allaah also says (what means): {And tell My servants to say that which is best. Indeed, Satan induces [dissension] among them. Indeed Satan is ever, to mankind, a clear enemy.} [Quran 17:53]

Abu Hurayrah narrated that the Prophet said, “It is enough as a sin for a person to relate everything that he hears.” [Abu Daawood]

Allaah knows best.