Hecabe has a name that to most people, almost entirely thanks to Shakespeare, is more familiar in its Roman form of Hecuba. She was the daughter of Dymas, king of the Phrygians, and became the wife of Priam, by whom she had nineteen children, including Paris, Hector and Cassandra. A lady of some consequence, therefore.
Her name, however, is not so straightforward. Like that of Hecate (with whom she must not be confused), it may mean something on the lines of 'far off, from hecas, 'far'. This could mean she was 'distant' in some way - perhaps having an influence from a distance, or producing a distant effect.
In one account she was stoned to death, and as she died turned into a bitch, later returning in this form to haunt the area where earlier her youngest son Polydorus had been murdered by the Thracian king Polymestor. This haunting could be regarded as a 'distant' influence.