YouTube Search: Go to YouTube and enter the channel name you have in mind into the search bar. Check the results to see if there is a channel with the exact name you want.
YouTube URL Check: In the address bar of your web browser, type in 'youtube.com/user/[desiredchannelname]', replacing '[desiredchannelname]' with the name you have in mind. If the page leads to an existing channel, the name is already taken.
Google Search: Google the name you are considering, followed by "YouTube channel" to see if any results come up with that exact name.