Why did Hans Landa in Inglourious Basterds change his mind about the "Jew Hunter" nickname?

It is probably not a change in heart, I am afraid! In the first case you are referring to when Col. Landa said the quoted statement while talking to LaPadite. The reason behind the sudden visit to his house was to search for the unaccounted-for Jewish family in that area. To remind LaPadite about his unofficial nickname was a tactic of Landa, I believe, to mentally pressure him to admit that he has given shelter to the Jewish family members (which Col. seemed to be quite sure of) and that could result in a disaster to both of the families by the colonel himself. This is a sort of act to tactfully make the victim mentally weak so that the victim gives in easily.

While on the other hand, the second scene you are referring to, he wants to terrorize some terrorists (apparently they are terrorists to him) who are not Jewish. So throwing the same dialogue would not result anything fruitful. Rather he should make sure in that situation that he must speak something that would make the prisoners think. He is more capable of doing something other than merely hunting or killing Jews, so that he must make himself sound like a frightening character to his enemies. This is also a sort of cunningness to frighten the prisoners.

Christian Rau's comment is valuable and worthy to be added. As he suggested in his comments, maybe Landa was preparing himself before the events to flee to the US. He also planned to make a deal with the Allies. So maybe to save himself, he started presenting himself as a good man who was just doing his job. He tried to mean that it was not his intention to kill the Jews, but his employer made him do that. In the end, he wanted to portray himself as just a responsible employee and nothing more!