Lukaku has been compared to the former Blues ace after notching his 50th goal in just 100 appearances in the Toffees 1-1 draw with Crystal Palace on Monday night.
The 22-year-old Belgian has often been compared to Ivory Coast legend Drogba but insists he is only intent on making his own name famous.
"Didier is my idol and he knows it but I am Romelu Lukaku and I am proud of my family name and I want to make my own story," Lukaku said.
"Of course I respect Didier a lot but I think there are differences in our style of play.
"I'm a young player, I want to play at a high level and help my team-mates.
"Hopefully at the end of my career I can say I did my best to create a name for myself."