aboutme.google.com) your channel is already disconnected form Google+. Learn more in the YouTube Help Center.
Note: as of January 9, 2014 this process will NOT work for newly created YouTube channels connected to a Google+ Profile or channels that have been connected to Google+ for longer than 14 days. If you don't want to use your real name on YouTube, you can ask YouTube support to disconnect your channel from your Google+ Profile and connect it to an existing Google+ Page instead.
Note: this is a slightly edited version of a post I originally made in the Google+ help forum in July 2013: YouTube & Google+: switch from a G+ Profile to a G+ Page identity / unlink your channel from Google+.