I assume you now have analog phone connected to the modem but want to move to SIP phone with gigaset.
Can say what is needed for Swisscom and assume you should get same info from Sunrise.
You need the sip credentials from your sunrise modem. With those you can connect the gigaset, or other sip phone. At Swisscom you can also get global sip credentials. With those you can use your sip connection everywhere. So you could pick up your Swiss phone while being in your second house in France or US as long as you have internet.

Seems like sunsrise cannot give you sip credentials. Maybe think of moving you number to other provider like sipcall.ch. Should be no problem to connect de phone to their sip server.