I should be able to do so with a static IP addresses, but I would like to know how to do it getting an IP address over DHCP. I thought that changing
/etc/resolv.conf would be permanent, but it dismisses the changes after a reboot.
I fixed this following the steps from cuonglm's answer on Unix & Linux Stack Exchange.
Edit the file /etc/dhcp/dhclient.conf and add
supersede domain-name-servers 184.108.40.206, 220.127.116.11;
Then restart network or run dhclient to make changes.
The supersede statement
supersede [ option declaration ]; If for some option the client should always use a locally-configured value or values rather than whatever is supplied by the server, these values can be defined in the supersede statement.