Your Chromebook or Chromebox is flooded with notifications from websites, any Android apps you may have installed, and even texts from your connected Android phone. Fortunately, with the “Do Not Disturb” feature of Chrome OS, you can mute the notifications.

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To enable the “Do Not Disturb” feature on your Chromebook, click the status area in the lower right corner that shows the Wi‑Fi signal and your device’s battery level.

Toggle the button labeled “Notifications”.

When you do this, your Chromebook will add a new pause icon to the status area to indicate that “Do Not Disturb” is active.

If Do Not Disturb is enabled, your Chromebook will clear all incoming notifications. Also, your computer will not display a message in the lower right corner of the screen for each new notification. You will still be able to browse all pending notifications in the list above the “Quick Settings” panel.
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If you don't want to disable notifications from all services, Chrome OS lets you specifically choose which apps and websites you want to disable.
Open the “Quick Settings” panel again and this time, click the small down arrow next to the “Notifications” label.

In the “Allow notifications from the following” list, you will find all apps and websites that can send you a notification. Uncheck the box next to an app or website to mute notifications from it.

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Make sure the “Do Not Disturb” switch is turned off, as it overrides your individual settings and automatically clears all notifications.
Information source: howtogeek.com
