My two cents
Based on the job offers of Swiss organisations and Linkedin Profiles of Swiss service designers that I could find, these organisations seem to have in-house service designers and therefore use Service Design:
Swisscom
Helsana
Swiss Re
Allianz
Groupe Mutuel
Zurich Insurance
Roche
Swiss Federal Institute of Intellectual Property IGE IPI
Federal Office of Information Technology, Systems and Telecommunication FOITT
City of Zurich
Raiffeisen
UBS
Crédit Suisse
Zürcher Kantonal Bank
ZHAW
Deloitte
Fjord, Accenture Song