My initial thought is that this needs to be set up in the backend as the activity name in the Event Log.

This is either a column containing strings which are in german language or in english language.

Whatever is selected there becomes the activity name. So this has little to do with the Celonis system language. You might be free to provide a mapping in SQL and translate them or use any other column in the source systems but that would be in data integration.

I am personally not aware of a possibility to support more than one language and then just switch in the frontend.

Exactly, this configuration needs to be handled in the backend. Depending on the process, and whether it's a standard or custom process, the activity table may already contain multiple columns for activities, such as "Activity_DE" and "Activity_EN." In that case, when configuring the data model, you should select the "Activity_EN" column as the activity name, rather than "Activity_DE."