Lukaku, who is currently on loan at West Bromwich Albion, has been likened to the Chelsea legend due to his style of play and physical presence.
However, the 19-year-old is keen to shed the tag of being the 'next Drogba' and make people remember his name.
"Didier and I have a similar playing style but I don't think he would have wanted to be compared to someone when he was young," Lukaku told West Brom's official website.
"Every player wants to be their own person, their own personality. I don't want to be the new anyone. At first it was okay - but I'm bored of it now. It isn't necessary and I don't like it now.
"I have my father's surname, I am Romelu Lukaku - I'm not anybody else. This is my own name and the name I want people to remember."
Lukaku has made just 12 appearances for Chelsea's first team, and has yet to score.