Well "hinn" is just the definite article... it's most commonly seen on the ends of words...
Úlfr - wolf, Úlfrinn - the wolf.
Maðr - man, Maðrinn - the wolf.
You could just translate it as "the".
Well, I'd say it isn't important whether a name has it or not, I guess it just depends on what has the best ring to it.
I have found that it seems "hinn" is far more commonly used for simple nicknames, nicknames of one adjective... The Old, The Red, The Black, The Grey, The Wise, The Lucky, The Mild...
But more complicated nicknames based on a story or something very specific won't have "hinn"... such as Snake-in-the-eye, Fairhair, Bloodaxe, Forkbeard, Hairy-breeches, Bluetooth. etc.
The last one would be Úlfr if it was Norse, that must be a modern Scandinavian spelling of the original Norse.