I understood my problem: I was using "Display Live results", which offers only options to use the entity label or a display mode of the entity.
I use now "Retrieve from server", which is a better option for me. The problem now is that I'd like to suggest only complete names, and not names based on different fields. If I use for autocomplete the fields indexed as "fulltext", I get suggestions for entities which do not exist. Example: I have one entity with Title = "Abiotrophia defectiva" and FieldA = "Streptococcus defectivus". In the search field I get suggestions like "abiotrophia defectivus", which is wrong and doesn't return any result. The best option would be to use for autocomplete the fields indexed as "String". But this type of index field is not available in the options of the "Retrieve from server" suggester.
pdau2571 → created an issue.