How to sort by title using Search API / fuzzy search?
Finally I got it working – here is how:

Search and metadata » Search API » fuzzysearch index » filter

First I checked the option "Aggregated fields" in the top section "Data alterations". Then I added an aggregated field that I called "Sort Name" pulling data from the field "Name".

Then I added that field to the list of indexed fields in the tab "fields". It is important to change the field type to "string" – otherwise the field won't be available for sorting. 

Then finally the field should be available for sorting from the "Sort by" dialogue inside the views form. 

The third paragraph of the accepted answer to the question "I have no fields available for sorting with Search API sorts module" pointed me in the right direction: "If a field is full-text, one trick is to create an aggregated field containing just that field and assign it a string type."

…I hope this may help somebody sometime…