A transmitted incident may contain many details: names, locations, conversations and surrounding circumstances. Not each detail becomes a binding qualification for the verse's legal or moral application. Sometimes only the legally relevant feature matters.
A general ruling illustrated by the case of one person may also apply to others who satisfy its conditions. The identity of the original incident and the scope of the ruling should not be conflated.
As a simple instructional example, a rule explained through the case of a traveller is not automatically restricted to that traveller's name or town, unless valid evidence establishes that restriction.