The first information Google asks you when you create your Google Account is your first name and your last name. And after that, it prompts you to choose your username.
It is easy to change your Google name easily which is your first name and your last and even middle name. But it not possible to change your username if it is registered with your Gmail Id.
If you want to choose another username for your Gmail account then you will have to create a new Google account with a fresh username.