The answer is Nikolai. Rimsky-Korsakov's father's name was Nikolai Andreyevich Rimsky-Korsakov. He was a nobleman and a government official in the Russian Empire. Nikolai Andreyevich had a great passion for music and played the piano and violin.
Mastering Mikhail Rimsky-Korsakov: A Musical Journey through the Life and Works of the Russian Composer