A friend's story would fit the conversation perfectly. It is funny, surprising or relevant, and you are tempted to tell it because the person is not there to contribute it themselves.
Consider whether the information was yours to share. Being told something privately does not automatically make it material for another group. Names are not the only identifying details; a workplace, location or distinctive event may make the person recognizable.
If you can ask beforehand, be specific about what you want to share and with whom. Permission for one conversation is not necessarily permission to post the story publicly or repeat it indefinitely. Accept a no without making the person explain why the matter is private.
When you are unsure, leave the story out. You can make a general point without borrowing the details of another person's life. The conversation will survive the absence of one excellent anecdote.
The same care applies to photographs, screenshots and messages. A friendly group chat is still an audience, and a private message may contain information the sender did not intend to circulate. Check before forwarding material that concerns someone else.
If you realize you shared something inappropriately, tell the person honestly, acknowledge the mistake and take reasonable steps to limit further sharing. Avoid promising complete removal where you cannot control every copy or recipient.
Ask about the audience and the form, not just whether the story can ever be mentioned. Someone may be comfortable with a quiet conversation between mutual friends and uncomfortable with a public post. Removing a name does not necessarily make a person unrecognizable, especially when the circumstances are distinctive. Give them enough information to make the choice, and accept a no without asking them to justify the discomfort.
If you have already shared something they wanted kept private, acknowledge the specific mistake and take reasonable steps available to limit further sharing. Do not promise that every copy or memory can be removed. Then change the habit that led to the problem. The fact that a story is moving, funny or flattering does not transfer ownership of the personal detail from the person whose life supplied it.
Trust often depends on these small decisions made when the other person is not present. You do not need to treat every ordinary mention as confidential, but you can develop a habit of noticing whose information is being used for whose benefit. A story can be entertaining and still be better left with its owner until they choose how, where and whether it should be told.
A little more room to be yourself.