You have a few choices, most of which have little if anything to do with your linux box.
1) Super Easy - Go into your router and tell it to alwasy give the linux box the same IP. To do this you usually need to tell the router/dhcp server the MAC address of the computer's network card. To find your MAC address, do this:
ifconfig eth0 (or eth1, or whatever eth you use to get online. If you only have 1, it is eth0).
It is possible that your router won't support static IPs, particularly if you have the cheapest of cheap routers. If this is the case, you can assign a static IP to your linux box. I don't know the path to the network config files in Suse, but it is likely close to Fedora. You would change to the network config file, and edit it from dhcp to having a staic address, and then give the static. You'll need to check out 2 files actually, the network config and the resolv.conf, which gives the nameserver addresses to your linux box. You'd have to do this:
(actual path may vary based on distro) vim /etc/sysconfig/network-scripts/ifcfg-eth0
Change it from:
GATEWAY=192.168.1.1 (assuming your router is at 192.168.1.1, if elsewhere just change it)
You'll also need to take a look at the file /etc/resolv.conf. That is where the nameservers are listed. your resolv.conf should have the current nameservers that the router is giving out. Just take a look at it, and copy the file to a backup incase it gets horked when you make this cahnge. Chances are very good your router is either giving out itself as the DNS server, or the DNS servers directly from your highspeed provider. You shouldn't have to actually make any changes to resolv.conf, just save the backup incase restarting the network services screws it up.
The only problem you might encounter in the future is if your high scpeed provider changes the address of their DNS servers in the future, and that is possible but very unlikely. You'll still have access to the net, but your computer won't be able to translate human names for websites (google.com) into IP addresses (18.104.22.168). If other computers in your LAN have connection but your linux box can't resolv names, this is what happened.
Now the final issue, restarting the network services. The other OS way to do this is to reboot the machine, and that will do it, but is a craptastic way of accomplishing what should be a 2 second solution. You have to be root again, and can give one of 2 simple commands. You can either do:
ifdown eth0 (followed by)
Or the even easier:
That should solve your issue. It is easier to tell the router to give you the same address, but it isn't at all hard to make your linux box come up at a given address on its own.