How can I stop my iMac from changing DNS settings automatically?

Uninstall the VPN as a test. Turning it off makes no difference as there are still files that launch on startup and continue to run in the background. You will need to follow the instructions for the VPN provider to uninstall to make sure all files have been removed. In most cases, simply dragging the application to the trash will not work.

If everything works correctly with the VPN uninstalled, you have now determined the source of the problem and know where to concentrate your efforts for a solution. Start by contacting the developer of the app or simply evaluate to reason why you are using a VPN altogether. If you have fallen for the marketing ploys that they provide security to your device, then that is a false assumption. Their use should only be to "tunnel" into enterprise networks such as those offered by work or school environments.

Remove the VPN entirely. The VPN is what's changing the DNS settings. Whether it's on or not is irrelevant. Many VPNs tend to bork network settings like this.

If you're unwilling to do that, all I can do is wish you luck.

Gareth Morris1 wrote:

I do have a VPN, but it is always off when I logon and has never caused this issue in the past.

Unless you're using a true VPN tunnel, such as between you and your employer's, school's or bank's servers, they provide false security from a privacy standpoint.  Read these articles:  Pubic VPN's are anything but public and Security Risks: The Dangers of Using Free VPNs (eccu.edu).  

Please follow Mac Jim ID's recommendation and uninstall the VPN fully. You can check to see if you've removed all of the supporting files by downloading and running the shareware app Find Any File to search for any files with the application's or the developer's name in the file name.  For VPN software you'd do the following search(es): 

1 - Name contains vpn

Any files that are found can be dragged from the search results window to the Desktop or Trash bin in the Dock for deletion.

FAF can search areas that Spotlight can't like invisible folders, system folders and packages.  

If you get warnings that the file can't be deleted because it is in use or used by another app boot into Safe Mode according to How to use safe mode on your Mac and delete from there.

Note:  if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode.  This makes it act as a wired keyboard as will assure a successful boot into Safe Mode.

Don't turn off the VPN, completely uninstall it. Turning it off does absolutely nothing helpful!!!!!

Remove the VPN entirely.

It serves no legitimate purpose if it's not being used to connect to a private network like your employer or school.

Your machine should get the DNS settings automatically from the router along with the DHCP address.

by default the dns ip is set by the hdcp Dynamic Host Configuration Protocol - Wikipedia functionality of the router your computer is set to

you can override that in the settings of your mac Change DNS settings on Mac - Apple Support

but some vpn clients could override that with whatever is the dns of the vpn server.

but yet, this have never ever happened to me in any windows version any macos version or any linux version and never having had any sort of VPN setup on any of those platforms it is with the information you have supplied the only difference between your setup and ours that we know of.