The name of your channel appears at the top of your channel above your videos (just below your banner art), as well as on each individual videos page.  It is the primary method, along with your custom banner art and icon, that a channel is branded.

If you need to change this name, you can do so in your Advanced Channel Settings section.  Once there, look for the link that says "change" to the immediate right of your current channel name.

On the popup window, hit "Edit" and it will take you to your Google "About Me" page where you can edit your channel's name.  Make whatever name changes you desire and hit "OK" when complete.

If your channel has a verification badge, please be aware that changing your channel name will remove the checkmark from your page, as this badge is tied directly to the name itself rather than your channel as a whole.  Depending on the current requirements, getting re-verified may not be possible.  Consequently, we recommend settling on a channel name prior to getting verified to avoid needed to change it afterwards.

Finally, please note that changing your channel name will not update your channel URL.