Hey you kids wanna see a dead body hear a completely unfounded bit of urban legend and speculation?
The reason Shuma-Gorath is at all popular or known is because of his appearance in 
the Marvel vs. Capcom games: Capcom picked the character for inclusion in the first Marvel Superheroes game because giant monsters are popular in Japan. Allegedly, when MvC3 came around, Capcom was very accommodating when Marvel asked them not to use certain characters (that's why Venom isn't in the game, for instance), but when Marvel said no to Shuma-Gorath, Capcom pushed back, insisting they be allowed to use him. So, basically, Capcom cares more about Shuma-Gorath than Marvel does. Keep that in mind: we'll come back to it.
As pointed out in today's review, Marvel owns the rights to Shuma-Gorath, free and clear: Robert E. Howard may have created the specific combination of words, but you can't copyright a name and so everything about the character 100% belonged to Marvel. And anyone - any article, any video, any message board comment, any corporate lawyer - that says different is verifiably, entirely, wrong. Shuma-Gorath was not the property of Heroic Signatures, the group that controls all of the old Robert E. Howard rights. The only way they own it now is if Marvel let them own it.
And here's where the wild speculation starts:
The first time Marvel said Shuma-Gorath was Gargantos was in Multiverse of Madness. Doctor Strange doesn't identify Shuma-Gorath by name in the movie, but the Lego set does, so we have a 2022 start date for when they began lying to you.
Around that same time, Marvel regained the rights to Conan the Barbarian for the first time since 1993. They re-introduced him in an Avengers crossover, and soon published Savage Avengers, a book that saw several Marvel characters teaming up with Conan to fight his old enemy, Kulan Gath. Smart fans who remembered the trouble caused by putting Rom: Spaceknight in the main Marvel U instead of his own continuity questioned whether this would be a problem in the future, but Marvel assured them it wouldn't be, suggesting they'd worked something out.
So here's our question: did Marvel trade away their rights to Shuma-Gorath, a character they created and owned but didn't care about (as we know from their dealings with Capcom), in exchange for the right to republish their own Conan appearances whenever they wanted? Because if they did, that's freaking stupid.
You can't copyright a name but you can trademark one. Since Shuma-Gorath was such a minor Marvel character beyond video games, it's possible that they didn't bother trademarking it before Heroic Signatures did. So even though Marvel owns the character's copyright they don't have the trademark on its name. That's why assorted Transformers had to have their names changed on toys or when Hasbro had to label some toys as "Marvel's [character name]" to be legally distinct. Marvel/Disney didn't even bother to license the name from Heroic Signatures for Doctor Strange 2: Multiverse Boogaloo. (They creature wasn't even named anything within the movie itself.) They just don't think it's worth possibly expending any extra money when there's a spare name it definitely trademarked that it could substitute.
https://comicbook.com/marvel/news/doctor-strange-2-shuma-gorath-why-marvel-cant-use-revealed/
So when we said that if an article tells you the character doesn't belong to Marvel then that article is wrong, did you think THAT specific article for some reason didn't count?
Notice that it emphatically does not say Heroic Signatures has the right to the name: it says the name first appeared in a Kull the Conqueror short (which it did), and from there it merely assumes that means ownership (which it doesn't). Even accounting for the difference between trademark and copyright, it's again a nuisance suit, because Marvel was the only one using the name for anything,
The closest similar case would be when IDW had to come up with different Dire Wraiths for Rom to fight: like Shuma-Gorath, the name "Dire Wraiths" pre-dated Marvel's involvement; so the name went with whoever owned Rom, but the visuals stayed with Marvel, and so IDW made their blue plant-zombie things.
Unlike Shuma-Gorath, Marvel's Dire Wraiths were created specifically under license to Parker Brothers. The work was done FOR Parker Brothers. (cf. Death's Head, Circuit Breaker, etc, in the Transformers comics.) In order to claim ownership, Heroic Signatures would need to prove 1) that the name Shuma Gorath was individually trademarked when it was published, and 2) that they've actively maintained that trademark since then. Nothing shows up, and they clearly made no effort to defend any such trademark through the decades-long span releases of various videogame, trading cards, and miniatures.
Take Heroic Signatures to court over it and they'd have to vacate their claim and pay any court fees, costing Marvel zero dollars total. And even if Heroic Signatures tried to drag it out, trademark doesn't stop Marvel from using the name casually. Like you said: "Marvel's Shuma-Gorath" would handily side-step any issues. And so we're still at the conclusion that the only way anyone other than Marvel can own the name Shuma-Gorath is if Marvel LET them own it. Because Marvel doesn't care that much about him...
You're correct that Marvel/Disney would recoup legal expenses in a trademark lawsuit since Heroic Signatures hadn't done anything with the Shuma-Gorath trademark (if they ever registered one to begin with). Your theory is that Marvel traded the name for the rights to be able to reprint its Conan comics without encumbrances, but what consideration does Heroic Signatures get out of that contract? HS doesn't have the copyright to the creature Marvel developed & the name is useless by itself. If there is no secret deal, why would Marvel/Disney abandon the Shuma-Gorath name when they have every legal right to it?
Being dumb and pointless is what MAKES a conspiracy theory!