Part of macOS
parentalcontrolsdFamily controls
○ Leave it
Applies Screen Time limits and Family Sharing rules.
What it is
Enforces content and time limits set through Screen Time or Family Sharing.
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
parentalcontrolsdParentalControlsFamilyControlsAgentfamilynotificationdaskpermissiondAskPermissionUI
From Procession’s guide, in the words the app shows.