We learn that Eliezer’s father name is Shlomo. What might have been Wiesel’s reasoning for including his father’s name only once in the book?

Eliezer's father's name is only mentioned once. As the narrator, Wiesel is telling his own story..... Shlomo is a very important part of that story, as his life and experiences parallel Elie's. In this way, Shlomo becomes a representative of all Jews.