Part of macOS
distnotedSystem messages
○ Leave it
Passes messages between apps and parts of macOS.
What it is
A post office for small system-wide notifications.
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
distnotednotifyd
From Procession’s guide, in the words the app shows.