Thanks Chris for getting back to me.
Yes, when I “Add Field” in the view editor, the custom fields are not in the list. In the list there are only three preexisting options under custom: “client_name”, “company_name” and “company_website”.
But the following seems odd and might help: If I add a new costum field by “Add New Field”, select “text”, Label “New Field”, Name “new_field”, save, then go back and click on this new field, the “Type” ist not labelled as “text” like the preexisting fields “client_name” etc. This would explain, why this option ist not in the list. But I don’t know why this is missing.