YOU SAID:

Luna is my name being cool is my game.

INTO JAPANESE

ルナは私の名前がクールなのが私のゲームです。

BACK INTO ENGLISH

Luna is my game where my name is cool.

INTO JAPANESE

ルナは私の名前がクールな私のゲームです。

BACK INTO ENGLISH

Luna is my game where my name is cool.