I see most of the place is using the "Display name", so why I need to set a Nickname?
Where it is being used?
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You technically don't have to set a nickname, it will be filled with your username if you clear the field out.
Display name is selectable between the user's username, first name, last name, first/last, or last/first, or nickname. The nickname exists to give you an option to set display name to something other than your username or real name.