This is a good question. There are many ways that Elie describes himself. We need to keep in mind that Night is his memoir. In light of this, the whole work tells us something about him.
First, Elie was religiously curious. Right from the beginning, an exploration of his faith interested him. He even sought people to help him learn more about his faith. This is an important point, because Elie possessed religious sincerity, a point that will be important in the book.
Second, Elie during the holocaust lost his faith. In the face of evil, he could not hold onto his traditional faith. Where is God in this evil? Here is what he says:
"For God's sake, where is God?"
And from within me, I heard a voice answer:
"Where He is? This is where—hanging here from this gallows..."
Third, we can say that Elie is a dutiful son. When sons abandoned even their fathers, Elie refused to do so. To the end, he was faithful to his father. At times he admits that he did so grudgingly, but he remained faithful.
Finally, Elie would probably view himself as a survivor. He not only lived, but he did not lose his humanity in the process.