While Zelda II: Adventure of Link was a direct sequel to the original NES game, the plot featured a brand-new princess Zelda despite having the same hero named Link. According to the plot, a wizard put her into eternal slumber because she failed to speak of the secret location of her father's triforce piece. So to revive the ancient maiden from mystical nap-time, Link must go find that lost triforce piece.
Since I could never stomach much of Zelda II, I never got to see the ending on my TV. But I'm guess I wasn't missing much. Have to give them credit for confusing fans with the 2nd game, most don't know about the different Princess Zeldas thing. Some players thought Link's name was Zelda for a long time.