The 19-year-old's style and physical presence at Stamford Bridge saw him draw comparisons with Drogba, who left for a spell in China in June.
Lukaku also moved away from London in the summer, heading to West Brom for a chance of first-team football.
And Lukaku, who is hoping to shake off an ankle injury in time for Belgium's World Cup qualifier against Wales on Friday, now wants to step out of the shadows and end the comparisons with the Ivorian striker.
"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 ok - 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 knows he still has areas to improve on in his game and hopes to continue his improvement at West Brom.
The Belgian admits spending time with experienced players like Frank Lampard and Drogba at Chelsea last season helped him to strengthen his game.
"I am of a young age - I have everything to learn," Lukaku said.
"I am left-footed but it can get better. I can shoot with my right but I want it to be as good as my left foot.
"I want my heading to be like Peter Crouch's heading. I want to do the maximum I can to achieve what I can. "At Chelsea, I used to stay behind every day with Lamps.
"We would work on finishing - with a competition as to who could finish the most chances. This was good fun but also important.
"Along with Drogba too sometimes, we would work on getting stronger in certain situations."
Source: team talk
Source: team talk