Hazard started in victory over Hull City on Sunday.
"I call him Eddie because it is easy, it is a nice nickname and he hasn't complained," said Mourinho.
"I don't know what I can bring but I know what I want from him. I want more responsibility and I want more ambition, because when you are a normal player you have to be happy when you perform okay, when you have some actions during the game that show your quality.
"When you have top talent you cannot waste that talent so I want to give him that ambition to be better and better, and to express himself on the pitch, match after match, not be up and down.
"He has the conditions to be a real top player. Football is full of top talents but not many top players. He is working very hard and I am very pleased with him. In the second part of pre-season in the States he was already coming in my direction and I am very happy with him."
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