Ultimately, the Night King's human identity may never come into play. He's just as likely to be a metaphor for the greatest enemy of them all: death. In an interview with Deadline, showrunner D.B. Weiss explained:
"I don't think of the Night King as a villain as much as Death. He is not like Joffrey, or Ramsey. He's not really human anymore. To me, evil comes when you have a choice between that and good, and you choose the wrong way. The Night King doesn't have a choice; he was created that way, and that's what he is. In some ways, he's just death, coming for everyone in the story, coming for all of us. In some ways, it's appropriate he doesn't speak. What's death going to say? Anything would diminish him. He's just a force of destruction. I don't think we've ever been tempted to write dialogue for the Night King. Anything he said would be anticlimactic."
The Night King may be the true god of death. And what do we say to the god of death? Not today.
It's no accident that the show's greatest villain is also its most mysterious. Whether there is a major twist in the Night King's story coming or not, he will remain the scariest monster of them all.