Final answer:
The third child of Marie, Countess d'Agoult, and Franz Liszt was named Cosima, inspired by St. Cosmas, which is not listed in the provided options.
Step-by-step explanation:
Marie, Countess d'Agoult had three illegitimate children with Franz Liszt. These children were Daniel, Blandine, and the third one, who was named after a saint. The correct answer to the question about the name of the third child is Cosima, which is not one of the options provided (a) Ludwig, (b) Wolfgang, (c) Franz, or (d) Amadeus. Cosima, although inspired by St. Cosmas, was not listed in the question's choices, which suggests a potential error in the question.