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.
Sonic '06 actually has some of the best story in the series. Shadow is at his peak, and Silver's story is good too. It's just Sonic's story (especially with Elise) and the gameplay that ruins it. Mostly the gameplay. But even with the gameplay problems, the level design is pretty good, as you can see if you play the Project '06 fan remake.
Region differences. Japan called him Eggman. But the US called him Dr. Robotnik at first to sort of make him more intimidating I guess. Both regions sort of merged the names over time.
"A race... A special race. There'll be something happening. Gawd. Do you see this? This is the diamond that I'm going to give to my brand new husband, and/or wife. It'll be theirs for the rest of time with the GameCube 2. So if you want--"
Fun fact about Eggman in Unleashed: there's this line in Mazuri (the Africa stand-in) where he says "I should've known you'd still be alive" to Sonic after having fought him in the Tornado earlier, but this was apparently a continuity issue that was caused by them introducing the Tornado segment into the game (I think Unwiished doesn't have it and thus the line makes sense?) But Eggman in that pre-boss cutscene before the Mazuri boss has no excuse for being perplexed; a competent player will take around 2 to 3 minutes to complete the level just before this.