From what I played of Sonic Adventure DX Director's Cut, he seems to like both. Robotnikland! The Egg Carrier! Eggmanland sounds dumb, but the Egg Carrier rocks hard. I can't choose.
If his name were being announced by, say, the Brawl announcer... I'd expect to hear "Dr. Eggman." He is a pretty egg-like man, is he not?