Have a Synology Diskstation at home which I among other things use as an OpenVPN server. When I’m traveling I enjoy being able to watch Danish TV without any geographical restrictions. I do this by having my OpenVPN profile (ovpn file) tunnel all traffic through the VPN incl. DNS. It also means that I can use it to safely browse if on a questionable wifi such as no-encryption hotel wifi or conference wifi. The two commands you need to add to the configuration generated by the OpenVPN server on the Synology (10.11.12.1 being by DNS in the house) is as follows:
dhcp-option DNS 10.11.12.1" redirect-gateway def1