Why do their nicknames include "Super Duper"?

Question

All the students have a nickname, and it always begin with "Super Duper".

Why do they use this as a nickname? Also, is this the correct translation for what it says in Japanese?

Answer 1

The reason they had these nicknames is to emphasize that Hope's Peak Academy is really hard to get into. Hence the students there are extraordinarily talented. It would seem that it's a requirement to have one outstanding feature to qualify for enrolment in the school. Apart from Naegi, who gained entrance through a lottery (and is the Super Duper Highschool Luckster)

Some liberties were taken in the translation much like other releases - for example the directly translated "Super High School Class Good Luck" doesn't roll off the tongue as easily as "Super Duper Highschool Luckster". It conveys the same message, but is perhaps not exact

A couple of the other changes to the titles and the rationale behind them in the fan translation are outlined here, similar reasons would apply to the official releases: http://danganronpa.wordpress.com/dr1/tl-notes/general/

Answer 2

I could not find a specific reason for them to use nicknames, guess it is just for plot reasons. Or even just cause they can.

As to how correct the translation is:

“超高校級の” is something like “super/hyper/mega/ultra highschool level/class”.

There have been quite some discussion on how accurate this translation is, but it is said that even though Super Duper sounds really stupid, it is the closest to the original translation.

A pretty nice article about this can be read here