The nmcli connection show command can be used to list your network interfaces.

~]# nmcli connection show
NAME  UUID                                  TYPE      DEVICE 
eth0  5fb06bd0-0bb0-7ffb-45f1-d6edd65f3e03  ethernet  eth0

Specifying a connection will show the settings for the connection.

]# nmcli connection show eth0 | grep -i dns
connection.mdns:                        -1 (default)
connection.dns-over-tls:                -1 (default)
ipv4.dns:                               10.14.15.7
ipv4.dns-search:                        example.com,stage.example.com
ipv4.dns-options:                       --
ipv4.dns-priority:                      0
ipv4.ignore-auto-dns:                   no
ipv6.dns:                               --
ipv6.dns-search:                        --
ipv6.dns-options:                       --
ipv6.dns-priority:                      0
ipv6.ignore-auto-dns:                   no
IP4.DNS[1]:                             10.14.15.7
IP4.DNS[2]:                             --

The nmcli connection modify <interface name> command can be used to modify one or more settings.

nmcli connection modify eth0 ipv4.dns "10.14.15.7,10.14.15.8"

After making a change to a device, the /etc/resolv.conf file may reflect the change. The nmcli device reapply <interface name> command can be used to get /etc/resolv.conf refreshed to have the change you made.

]# nmcli device reapply eth0
Connection successfully reapplied to device 'eth0'.