The only part of you that is truly "you" is the part that actually experiences, ie your awareness, and your true intention. Your awareness never truly sleeps - even when you are deeply asleep you have awareness, although it is all inward. Only a general anaesthetic can properly turn it off.
Up to this point, you may have considered your thoughts were "you", but they're not - they're simply your ego in action - it is responding to data that is either fresh from the senses or equally as often from memory. You are aware of this because your own thoughts can upset you, are not what you want to think, are nonsense or completely contradict each other. They are not your intention, which is to do with self-worth, safety and creation.
Most people will spend their entire lives on autopilot, not being truly themselves but being controlled by their ego. This is fine if your default attitude is bright and sunny - why wake up from a good dream? Unfortunately most egos are not! They are fearful, sad, lonely or bitter, and for many life is spent trapped in a dream of disappointment, which by their behaviour they inflict on the next generation.
There are a few people who are so sick of being sick of it that they become determined to find a way out of their own negative thought, and it is these people who discover ways to override their egos and discover true happiness - not from the world around them but from within themselves. Such a discovery is called many names, such as awakening, enlightenment, epiphany or self-realisation.
It is beyond the scope of this introductory article to point you fully in the direction of being liberated from your ego and learning to control it rather than vice versa. However, most sources agree that the first step to liberation is learning to calm the mind. A calm mind turns off the ego and you can begin to see things clearer.
A final point - your ego is not your enemy. It is there for a good reason - to help you survive, and enable you to multitask. It is a wonderful servant, but not often a good master. Learn to tame it, and your life will be powerful indeed.