especially since canonically (in SA1) Sonic started calling him that to make fun of him and he just went with it. on the one hand props for just saying to the haters "you have no power here", but at the same time like... breh?
It's a Resident Evil VII: Biohazard situation. He's always been Eggman in Japan. Sega of America, being a weirdly independent and opinionated entity from Sega of Japan, made up a whole ridiculous backstory about "Ivo Kintobor," and that influenced the US manuals, future translations, the SatAM cartoon show, and to a lesser extent the Archie comics.
The exchange in Sonic Adventure was Sonic Team proper trying to syncretize these localization differences. Unfortunately, unlike Resident Evil being called Biohazard in Japan, Doctor Robotnik is blatantly the cooler name for the character, even if it is a cold-war relic.
Modern Eggman: "You're not in a position to demand anything, you nasty little pincushion!"
Modern Tails: "Eggman! How?"
Classic Eggman: "He had a little help."
Classic Tails: "Dr. Robotnik!"
Classic Eggman: "Oh, nobody calls me that anymore."
"Please, don't call me by my name. I will exclusively be referred to by a rude nickname given to me by my mortal enemy. I talked to the future version of myself and we both agree it's the way better name." ??????
I dream of one day buying Sega and declaring that the series will now officially be following a new canon taking place on Mobius which is threatened by Dr. Robotnik.
And yeah.. at this point the only reason the Eggman name is so prominent is because of Sega's contempt for any western element of the canon.