Proper nouns normally go with out articles. But when the named one is unknown to the speaker we use indefinite article before it. Moreover when a special characteristic of the named person strikes us most we use article before proper nouns.
We are speaking about the poetic qualities of one in both the examples with the difference that in the first you'll come across only one as such while in the second there are many.
In the above examples our eyes were inverted for the soul searching of Henry; a Henry who is sadistic who derives hellish pleasure out of others' sufferings, and this quality gets the upper hand over his other qualities a man is an odd assortment of. Hence indefinite 'a'/'an'.
In the second you have already pinpointed on the sadistic nature of Henry to the exclusion of all other qualities in him and like to dwell on it at length. Hence definite 'the'.
The adjective, 'sadistic' limits Henry and "a/an/the" preceding 'sadistic' determine one Henry of sadistic nature. Articles determine whether his sadistic temperament is well defined or just one in the anonymity of his many more qualities.