Hi,
Which one is correct? Both.
When do we use "in the list" and when "on the list"? Often, there is no difference, although we usually say 'on'. However, here are a few thoughts.
1. Is your name on the list?
A. The list of people accepted to go to Oxford is on the notice board.
B: Oh, I hope my name is on the list! I really want to go to Oxford!
Here, B is thinking less of the physical list and the words written on it, and more about the purpose of the list.
2.Is your name in the list?
A: I don't know, it's not on page 1, let me look at page 2.
Here, I'm thinking of the list as pieces of paper with words on them.
Best wishes, Clive