The current possibilities of defining a name server when serving as DHCP Server is limited to IP addresses:
[[ https://docs.vyos.io/en/sagitta/configuration/service/dhcp-server.html#cfgcmd-set-service-dhcp-server-shared-network-name-name-name-server-address
| https://docs.vyos.io/en/sagitta/configuration/service/dhcp-server.html#cfgcmd-set-service-dhcp-server-shared-network-name-name-name-server-address ]]
The system name server can also be the received name server of any interface that's been configured as DHCP client and has sucessfully configured that way. BTW, the documentation is not representing all options VyOS itself offers.
[[ https://docs.vyos.io/en/sagitta/configuration/system/name-server.html#cfgcmd-set-system-name-server-address
| https://docs.vyos.io/en/sagitta/configuration/system/name-server.html#cfgcmd-set-system-name-server-address ]]
It would be nice to have the name server pushed by the dhcp server to be the name server received by a specified interface.
There are cases where DNS forwarding will not work as workaround, e.g. when using a container like adguard, that needs to have its upstream DNS servers point to an IP address, whereas the localhost does not work.