goddess. She was associated by the Greeks with the moon, and her parents were Perseus or Zeus and Demeter. For a goddess associated with the moon (and later specifically with Artemis) her name can be more confidently interpreted as 'she who has power from afar'.
This refers not only to the rays of the moon but to her special power as a giantess. The name was also one of the many by-names of Apollo and his sister Artemis.
In this respect it is worth noting that the Greeks quite often formed names from the by-names of other gods (but only very rarely from the real names), and it might almost be that this particular by-name somehow became detached from Artemis and became a separate moon goddess. Robert Graves and others, however, derive her name not from hecatos, 'far' but from hecaton, 'hundred'.
This could refer to a hundred of a number of significant things: victims on her altars, years during which unburied souls were detained, months of a king's reign, multiplicity of a harvest (a hundredfold), and the like. Either way, whether 'far-darting' or 'a hundredfold', she has a powerful and impressive name.