He was always already registered as J, but not under his actual name. That's why he didn't want to admit to being registered at first, because that would give away the game. He becomes the top ranked again because he killed a few monsters during the year and garnered enough points to be considered number 1. It automatically included him and tallied his points as soon as he got out of the rift. He can then also register under his own name as a second registration.

I'm confused. At the moment I am at chapter 18. But I don't understand how and why J now is registrated. He was just watching an ad at the end of chapter 13 and in chapter 14 he is the top ranked. When and why did he do that?
Please help me understand (⊙…⊙ )