GamerGen (French) wrote article about this, mentioning that if Game Freak is involved but not The Pokémon Company, it should be related to the main games and not the TCG. Are they right about this?
This is a bit confusing to me, although I'm almost sure it will have something to do with Ultra Sun/Ultra Moon because of that name, it's really intriguing.
No. They are absolutely wrong.
In Japan, Nintendo, Game Freak and Creatures Inc. are the three co-registrars of every Pokémon related trademark.
Here are a few examples over the past few years
Cosmog
Phatom Gate (A 2014 Japanese TCG set)
PokéDaring (An augmented reality attraction in a theme park in Japan)
Pokémon Sun & Moon (Video Games and TV series)
Splash! Magikarp (A mobile game name)
Tokyo DX (The name of one of the new Pokémon Center stores)
Ultra Necrozma (A Pokémon form)
Outbreak (An event in Yokohama each year: Pikachu Outbreakchu)
Z Power Ring (An item used in the game and for merchandise)
PokéNano (A merchandise line akin to Lego)
Pokétabi (A merchandise line)
Pokémon Boxercise (An attraction at the Pokémon EXPO Gym event)
Event Organizer (A title of people who organise TCG events in Japan)
Ash's hat
I can go on for days listing all the obscure and varied trademarks. All of these were trademarked by all three companies. That's what happens in Japan. The Pokémon Company doesn't register trademarks.