It’s a bit of a joke now how many times his name appears before you play the game but he’s earned it because he’s an excellent director which makes very distinctive narratives, styles and snappy but deep gameplay.
And he doesn't just bombard you with his own name. I remember playing Death Stranding, and every time a new character is introduced for the first time, in a cutscene, there is a movie-style text appearing with the character's name and their actor's name below, e.g. "Sam - Norman Reedus", in the same style as Kojima's own name. Except for him instead of character name + actor name, it is usually "Director - Kojima", then "Producer - Kojima", etc.
Realistically though, his games aren't as mainstream these days, and I doubt that a giant chunk of modern gamers (in the 15 to 22 range) have played any of his games. Which makes me think it definitely isn't due to those "10-second bombardments of his name" at the beginning of his games.
You really need to play MGS1-4 to appreciate the story and gameplay, and to get a real sense of Kojima's brilliance. They're top notch all around, but definitely up there as one of the best stories ever told.
Correction: Survive is the worst if you even want to consider it a MGS game
Kojima's team was making an initial prototype, didn't like how it came out, and then handed it over to Platinum Games. PG completely reworked the entire thing, and imo it came out great.
For the record, Platinum Games are known for amazing works like Bayonetta series, Nier: Automata, and plenty others. The founders of that studio were also heavy-hitters before forming the studio, with Hideki Kamiya being the director of Resident Evil 2, Devil May Cry (the original, not the reboot), Vietiful Joe, and Okami.
P.S. Survive is by far the worst game and isn't even comparable to anything else. It was made after Kojima quit though, so it is difficult to even consider it a legitimate MGS game.
Earlier games would just have cheeky references to himself here and there. Most obvious one I remember was Psycho Mantis' fight in MGS1 opening with him appearing to change your television input to one called "HIDEO" (instead of "VIDEO").
It's meant to be like a tv series, just like how Game of Thrones or The Wire flashes the directors name before an episode.
Just how MGS 3 was meant to be a James Bond style movie so starts with a female vocalist singing a overly passionate ballad. They're stylistic elements from cinema, and in that case TV he's bringing to gaming to set a tone.
His justification being that he wanted them in the game but didn't want to take time away from their own works.
He fought his way to where he is in the late 80s, early 90s from nothing [1]
The idea that you shouldn't be proud or shout about your achievements is a technique loser adults push on children to stunt their potential.