His name has gone through a few changes since his creation. Prior to the Dreamcast, he was always known as Dr. Eggman in the Japanese version and Dr. Ivo Robotnik in the Western version. In Sonic Adventure 1, they subtly tried to change his English name to Eggman by having "Eggman" be an insult made by Sonic and co. that just ended up sticking. Sonic Adventure 2 is when they brought the names together by creating the characters Gerald Robotnik and Maria Robotnik, and by having everyone, including Eggman himself, refer to him as "Eggman".
He's always going to be referred to as Eggman from now on, but technically, his name IS Ivo Robotnik.
Hope I helped you out there.