From the YouTube home page, select "sign in." This is located in the upper right hand corner of the page. This links you to a Google account page where you enter your login information. After entering your account information, the page redirects you back to YouTube, where you can then see your profile image in the upper right corner.
From your profile image in the upper right hand corner, a small pop-up box opens with your profile image, a link to your Creator Studio page, a cog wheel and a sign out bar. Select the cog wheel to open your YouTube settings page. It is located to the right of the Creator Studio bar.
The YouTube settings page opens to an account information overview page. To the right of your name is a link to edit on Google+. Select the link to load your Google profile page. In Google+, you can edit your name and include a nickname. It also lets you review how the site displays your name.