DNS problems when using L2TP

I’ve seen issues where if the private network you’re connecting to uses a “.local” domain, you MUST use the fully qualified name. E.G. hostname.company.local or it will not resolve.

Try that. It’s what I have to do when connecting via VPN to my company. Windows machines can just use “hostname” and it will resolve.

When I occasionally use a VPN, I use "Private Internet Access" as the provider and it handles the DNS without problems. I say this because it's possible your VPN provider isn't handling DNS properly. As a test, perhaps you could try a different VPN to see if it's related to the VPN handling of DNS rather than believing the problem is with macOS.

Same issue here, but with iOS 16.6.1. VPN server is SonicWall and with Mobile Connect under SSL it works fine. Checked the connection under L2TP/IPSec and DNS doesn't work. The network is working, due if I check any web under the IP, it works. Checked the same config under Android 11 (configuring manually the VPN) and DNS works fine. It's not the VPN provider... :9

As the VPN is not an Apple product, you need to talk to its developers. They are responsible for making their product work with macOS not the other way around.

If you search this community, you'll find many posts concerning VPN usage. Pretty my universally, the use of a VPN is discouraged for all the various reasons listed.

If your employer, or some other agency you must deal with, requires a VPN, then you have to use it. But that's a different thing altogether.