In order to change your name on a YouTube channel:
Sign in to YouTube.
On the upper right, just click your profile photo and go to Your channel.
Click "Customize channel".
Go to the "Basic info" tab.
On the right there is a pencil next to your name.
Add your new name and press the button Publish.
Note: This will also change your Google Account name in case your channel is associated with a Google Account.
It normally updates immediately, yet in some cases it can take a few minutes to be reflected everywhere.
