Ok but how would he know.
He’s been trapped in a puzzle for 3000/5000 years, right? Was he even conscious in there? How could he hear all the things people were calling him over the ages? And where did he even get “Yami”?
Because I like to think he spent the first few weeks after the puzzle was solved floating around at Yugi’s shoulder like “Who the fuck am I.” And at some point he overheard Yugi’s grandpa explaining the lore behind the puzzle, like:
Solomon: Legends say that this puzzle belonged to an ancient Egyptian pharaoh!
Yami: Sounds legit. That could be me, right? I feel vaguely pharaoh-y.
Solomon: And the hieroglyphs in the tomb where the puzzle was found spoke of a “King of Games!”
Yami: That’s a super cool title, I’m keeping that one.
Solomon: And the inscription on the puzzle reads “The one who solves me shall gain the powers and knowledge of darkness.”
Yami: Guess that’s me. I’m the darkness.
And when Yugi finally gets around to asking him his name he’s like “Ah, yes, my name. I have…many names. So many names. That I remember. Like…Pharaoh. And…King of Games. And. Uh. Uh… *looks down at the puzzle* dARKNESS.”
tldr; “Yami” was totally a line-of-sight name he got stuck with.