Part of macOS
appstoreagentApp Store updates
○ Leave it
Downloads App Store updates and purchases.
What it is
Handles App Store downloads, updates and purchases in the background.
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
appstoreagentcommercestorekitagent
From Procession’s guide, in the words the app shows.