I'm honestly kinda shocked we haven't gotten a desert stage yet. Gerudo Valley is the closest thing, but its merely close to a desert, not a desert in of itself.
...oh, I guess there is Mushroomy Kingdom. That's a desert, yeah.
Trademark renewals are irrelevant. They're renewed to keep the trademark even if they aren't used.
King K. Rool did not have a registered trademark btw. People overreacted to that. A standard trademark is still interesting, as its the company claiming that name as a trademark of said company. However, registered trademarks are more important. King K. Rool has never had a registered trademark. (I think this past year, Dixie Kong and Cranky Kong got registered trademarks, for example. Donkey Kong and Diddy Kong have had them for a long time.)
That being said, Golden Sun is a registered trademark of Nintendo because its an intellectual property with a unique name and branding (Kirby is not a registered trademark because Kirby is actually a proper name, for one example).