Final answer:
The phrase in question is a complex sentence as it includes one main clause and one subordinate clause.
Step-by-step explanation:
The grammatical name for the phrase 'what saddens me the most is the fact that he died' is a complex sentence. This is because the phrase consists of one main clause, 'what saddens me the most,' and one subordinate clause, 'the fact that he died,' which cannot stand alone as a sentence. A simple sentence has just one main clause, a compound sentence has two or more main clauses, and a compound-complex sentence has two or more main clauses and one or more subordinate clauses.