"Itsumi Mario" makes no sense
It's always fun when people use their creativity to come up with goofy theories that don't hold any water, but sound 'right' on the surface, but this is just too much.
First, none of the games were EVER called 'Itsumi' anything, not in katakana, hiragana or kanji.
Second, 'Super' in japanese is not 'Itsumi', it has always been written as katakana-english as 'SUUPAA' (スーパー）.
Third, japanese intonation of 'Itsumi Mario' would sound COMPLETELY DIFFERENT from the CLEARLY (mock-)ITALIAN intonation of 'It's me, Mario!'. It would not sound the same AT ALL, it would not sound italian whatsoever.
Fourth, there are more syllables that wouldn't make sense with 'I-TSU-MI'. What Mario says in that italian-sounding accent and intonation, would be phonetically 'I-TO-SU-A-MII'. He doesn't say 'It's me', he sas 'It's-a-me'.
Fifth, japanese 'Itsumi Mario' would sound and look so different in all possible ways, no one could EVER confuse the two.
Sixth, if they were to use japanese, why would they use 'Bros.' at the end? That's a weirdly contracted english word, so if they were ready to replace 'Super' with a japanese word, then why is 'Bros.' still english, and not 'kyoudai' or something?
(Japanese has SO many words for these things, by the way, that many times things can't be directly translated, because you have to interpret and choose which word you need to use, and often, there's no 'clear choice')
This character, the games, the movie, etc. are NOT called 'Itsumi Mario Kyoudai', but 'Super Mario Bros.', so it would _ABSOLUTELY_ make no sense to interpret 'It's Me, Mario!' as 'Itsumi' anything.
Seventh, if you can believe that, the word 'Itsumi' ends with a SHORT wovel, not a long one. Japanese is very strict with short and long wovels, they sound completely different.
English, however, doesn't have that many short wovels, so anything can be 'stretched' and it seems fine. That's why even though 'Tokyo' is written with short wovels (erroneously - it should be Toukyou, Tookyoo or Tōkyō in Rōmaji, as it IS とうきょう in hiragana and 東京 in kanji), which has allowed really awful and unrealistic transliteration of japanese words, so they became butchered in english.
In japanese, 'mi' and 'mii' sound completely different, whereas in english, 'me' sounds like 'mii', and there's no way to really write the 'mi'-sound (and 'mee' would sound identical to 'me').
So if this stupid, stupid non-theory was correct, it would be 'Itsumii', not 'Itsumi' in any case, so it CAN'T be that for this reason alone, not to mention all the other ones I listed.
Eigth, if this was the case, WE WOULD FRIGGIN' KNOW ABOUT IT BY NOW, it's not some secret reality that only some TikTok (censored) can unravel and expose for the whole world to see. There are 'secrets' that people don't realize, as in 'no tears' means the kind of tear you can do to a paper, not the kind that comes out of an eye and so on.
However, this stupid thing is NOT one of those, it's just some turd-for-brains getting a ridiculous shower thought and then 'revealing' it to the world without thinking, researching or knowing anything about japanese language, culture or the character they are talking about.
Thus, this whole thing makes NO sense whatsoever.