Part of macOS
NotificationCenterNotification Centre
○ Leave it
Shows notifications and widgets.
What it is
Draws notification banners, Notification Centre and desktop widgets.
If you stop it
macOS starts it again straight away. Leave it.
The verdict
○ Leave it. Part of macOS, or something that starts again by itself. You never need to close these.
In Activity Monitor
NotificationCenter
From Procession’s guide, in the words the app shows.