DNS settings changes after shutdown

Reset the NVRAM and reboot, failing that delete the connection create a new one:

Open network preferences under >System Preferences/Network

unlock the panel with your administrative credentials if you need to

select the service:

delete the service by clicking "-"

then create a new service by clicking "+"

Create a new interface and use the default name

then configure as needed, then reboot.

if the problem persists either try with a new account or repeat the previously outlined steps after doing this:

Shut down, then disconnect all external devices

reset the smc

https://support.apple.com/en-us/HT201295

reset the NVRAM

How to reset NVRAM on your Mac - Apple Support

then boot into safe mode

https://support.apple.com/en-us/HT201262

then reboot normally with devices disconnected.

Make sure you have set up location as automatic , set WPA2 Personal , and saved a password for wireless network in the setting , do not enable proxies .

Once google DNS server settings ( 8.8.8.8 and 8.8.4.4 ) are added by clicking on plus sign you have to click on ok .

Then come to the first page and click on " apply " to get the setting saved .

Enter those settings again, then immediately restart in Safe Mode. See if the settings stick (I expect they will). Then restart normally again. If they stick now then you’re probably ok.

Let us know.