The names in the data source are partially translated via the Swisssearch endpoint (/rest/services/ech/SearchServer?type=locations). Unfortunately, this is currently only the case for municipal boundaries.
For example:
Simplon / Sempione
swisssearch gg25
https://api3.geo.admin.ch/rest/services/ech/SearchServer?sr=2056&searchText=sempione&lang=de&type=locations&origins=gg25
https://api3.geo.admin.ch/rest/services/ech/SearchServer?sr=2056&searchText=Simplon&lang=de&type=locations&origins=gg25
vs
featureseach ch.swisstopo.swissboundaries3d-gemeinde-flaeche.fill
https://api3.geo.admin.ch/rest/services/ech/SearchServer?sr=2056&searchText=sempione&lang=de&type=featuresearch&features=ch.swisstopo.swissboundaries3d-gemeinde-flaeche.fill&timeEnabled=false
https://api3.geo.admin.ch/rest/services/ech/SearchServer?sr=2056&searchText=simplon&lang=de&type=featuresearch&features=ch.swisstopo.swissboundaries3d-gemeinde-flaeche.fill&timeEnabled=false
To enable a multilingual search, unfortunately the only option at the moment is to construct the search query in multiple languages on the client side and to send it in this form. However, a multilingual query of this kind must be sent to the swisssearch endpoint.
This supports fuzzy search and returns a response if the search text is in multiple languages:
https://api3.geo.admin.ch/rest/services/ech/SearchServer?sr=2056&searchText=Wallis,valais&lang=de&type=locations&origins=kantone
https://api3.geo.admin.ch/rest/services/ech/SearchServer?sr=2056&searchText=Simplon,Sempione&lang=de&type=locations&origins=gg25