Koopaling fan boy here. The reason they have different names is because the cartoon was in production before they had official names. Nintendo of Japan didn't actually name them in their debut (they were however depicted as Bowser's children's in the manual regardless how many people try to deny that.. I looked up the scanned pictures with translation). Nintendo of America gave them their names after the cartoon was already finished and Japan decided to keep the names. Other characters like Villager and Rosalina however will have different names in Japan and maybe other countries. In some countries, they will also be known as "Bowser's Minions" instead of the Koopalings, which I prefer the latter. The names in the cartoon are :
Larry - CheatsyMorton - Big MouthRoy - BullyWendy - Kootie Pie
Ludwig - Kooky Lemmy - Hip
Iggy - HopI might have gotten Hip and Hop mixed up but aside from those two, I actually think the cartoon may have done a bit of a better job at giving them quirky names that go with their personalities.edit - sorry the body of this post is so messed up.... the forum adjusts it on its own so everything looks sloppy now.