Technically his name is Dr. Ivo "Eggman" Robotnik, but the name Robotnik is so rarely used (The last time a Sonic game even mentioned it beyond occasionally name dropping Mean Bean Machine was the first Sonic Riders game and that was only in text descriptions) that it might as well not exist.

Even in the comics which normally are allowed more leeway than the games, even characters who it would make more sense to call him Robotnik than Eggman (Like anyone in the Classic Era timeline, Fang especially.. or Dr. Starline in the Modern Timeline who worships the ground Robotnik walks on), the name Eggman is exclusively used.

The only media that treats Robotnik as his name and Eggman as a nickname is the movie, the same movie that wanted to call Sonic's World Mobius, but Sega wasn't having that. (Sega's a xenophobic company that fought hard to take away Sega of America's creative freedom and they're not about to let the name Mobius or the Freedom Fighters sneak in the back door.... to such an extreme that Mobius has to be called "Sonic's World" according to Sega Mandates)