Part of macOS
mDNSResponderNetwork names
○ Leave it
Finds websites and devices on your network by name.
What it is
Turns names into addresses, and finds printers and other devices nearby.
If you stop it
Internet and network names stop working for a moment. 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
mDNSRespondermDNSResponderHelper
From Procession’s guide, in the words the app shows.