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.
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?
"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.
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.