I searched around a bit, and found a “SlowFuzzyQuery” in a sandbox version of lucene (maven, javadoc).

This SlowFuzzyQuery is able to do, what I need, but is a bit slower (which is not a factor for me). May you implement this class into your QueryBuilder (org.hibernate.search.query.dsl.TermContext.QueryBuilder). I would highly appreciate this, because it would give me the possibility to uses custom analyzers, what I can not do without the QueryBuilder.
Example code for current usage:

this.fullTextEntityManager.createFullTextQuery(new SlowFuzzyQuery(new Term("NAME", "SEARCH_TERM".toLowerCase()), minimumSimilarity), CLASS).getResultList()