If your YouTube channel is currently unlinked from Google+, from time to time when you are using YouTube you will see a popup that prompts to update your YouTube channel identity.
If you do not wish to currently update your YouTube channel identity, you can decline that option.
How you do that depends on exactly which prompt you are shown. See the examples below for more information on what the various choices mean and how you can at least temporarily dismiss the popup.
The first example is a popup that is titled New choices for your channel name
You likely will only see this prompt if you are not using Google+ on your YouTube channel's Google account.
It provides several options:
• If you would like to temporarily dismiss the prompt, click the X in the upper right-hand corner of the box.
• "Use your YouTube name on Google" with your YouTube username shown.
This option creates a new Google+ Profile using your YouTube username. Your Google+ Profile identity will be used across Google, including your Gmail email account, so if you don't want your messages to look like they are being sent from your YouTube channel, don't choose this option.
• "Use your Google name on YouTube" with your Google profile name shown.
This option creates a new Google+ Profile using your current Google profile identity. Because Google+ Profiles must comply with Google+ Profile names policy, you shouldn't choose this option if your current Google identity is your business, band name, brand or celebrity name, and you don't want to use your real name for YouTube, Gmail and other Google products.
• "Update your name" and use your updated name on both YouTube and Google.
This option creates a new Google+ Profile with a name you choose. As I've mentioned above, the name must comply with the Google+ Profile names policy.
• "I want two different names - one for YouTube, one for Google"
Clicking this link down at the bottom of the popup window will dismiss the popup and should tell YouTube you want a different option than using the same name everywhere on Google.
If you choose to not link your YouTube channel to Google+, you will be shown popups with additional options that allow you to link your YouTube channel to a Google+ Page, rather than a Google+ Profile.
Also see: What does it mean when you see a popup headed "YouTube is updating your channel's account"?
If you linked your YouTube channel to a Google+ Profile and would like to unlink it again, here's how you do it: