I've been unable to find anything about this handsome Prince Gorchakov except the dates of his birth and death - 1875 and 1916 - and that in 1904 - the year this portrait was painted - he married Daria Mikhailovna Bibikova (1883-1962), a lady-in-waiting to Empress Alexandra Feodorovna. The year of his death and his relative youth - he would have been only forty-one - leads one to wonder if he may have been a casualty of World War I.
Nikolai Petrovich Bogdanov-Belsky (1868–1945), Russian painter whose work consists mainly of portraits, genre paintings, and landscapes. Born in the village of Shitiki in the Smolensk region, he studied art at the Semyon Rachinsky fine art school, icon-painting at the Troitse-Sergiyeva Lavra in 1883, modern painting at the Moscow School of Painting, Sculpture and Architecture from 1884 to 1889, and at the Imperial Academy of Arts in St. Petersburg from 1894 to 1895. He later worked with studios in Paris. Active in St. Petersburg, he was a member of several prominent societies and became pedagogue and academician in 1903; he was an active Member of the Academy of Arts. After 1921, he worked and lived exclusively in Riga, Latvia. He died at the end of World War II, in Berlin.