"Olympic" is a trademark. :)

[Query]

There have been many organizations that ran their own events that they called "Olympics".

But, in the U.S., "Olympic" is a trademark of the U.S. Olympic Committee.

  https://www.teamusa.org/brand-usage-guidelines

I think the International Olympic also owns some trademarks - including some of the same trademarks.

So, you want to run a "Barbecue Olympics", "Oregon Spelling Bee Olympics", "Midtown Ice Rink Olympics", or create an Olympic videogame, maybe you need the permission of the USOC and/or the IOC.

Perhaps if Olympia, Greece (the site of classical Greek Olympic games), decides to run their own "Olympic" games again, and markets it in the U.S., they would need permission too.

Could a business or sports team call itself "Cherokees", trademark it, and bar the Native Americans of that tribe from using that term?