Part of macOS
Wallpaper…Wallpaper
○ Leave it
Draws your desktop picture, including moving ones.
What it is
Shows the desktop and lock-screen wallpaper. Moving wallpapers use more energy.
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
Wallpaper…
… means any name that starts this way.
From Procession’s guide, in the words the app shows.