The wordplay here is Coup with Koopaling; because these guys are trying to dethrone Bowser.

Story so far for them? Umm...
Fanon idea that Historically Koopas used to be ruled by 5 Royal Houses, but Bowser's Father (being twice as evil as Bowser) sabotaged the other four Families and banished them leaving their youngest offspring orphaned. So Bowser doesn't know about this, thinking his liniage was always the one and only, while also giving the Koopalings a complete origin story.
And now these four have come for justice! And it'll be a fight of Koopalings vs Coupalings! Brother against Brother! You can probably already see the family resemblances.

Maybe more detail will be provided in singles of each one of them, most likely. (also, I know I already made a Koopaling-guy with the name Kurt already, but that name is too perfect not to use in THIS. So I'm torn, okay?)