Are you using NetworkManager or traditional method to manage your network devices? You can find this out in YaST->Network Devices->Network Settings->Global Options and its under “Network Setup Method”.
If you control your network with a network manager, there is a spot there for inserting the DNS Name Resolvers, you also have to put in the IP of the gateway, much the same location in the GUI. If you control your network via Yast (so-called traditional method with ifup) there is a place for the DNS Name Resolvers there too, and the gateway.
For example here’s the Yast/ifup one: Adding Name Servers and a Gateway to your IP configuration