Hello,

With the older Ubuntu distributions, you could do that with the /etc/resolv.conf however, with Ubuntu 18.04 you should make the change in the netplan configs at /etc/netplan/*.yaml files.

The file would look something like this:

network:
    version: 2
    ethernets:
        eth0:
            addresses:
            - 123.123.123.123/20
            - 10.0.0.0/16
            gateway4: 123.123.123.1
            match:
                macaddress: cc:8c:11:e1:1b:81
            nameservers:
                addresses:
                - 8.8.8.8
                - 8.8.4.4
                search: []
            set-name: eth0

To change your nameservers, just update the addresses under the nameservers section. And then run:

sudo netplan apply

Hope that this helps!
Regards,
Bobby