Katun is a river
The Katun' river is the main water artery of Mountain Altai. Katun' is also the largest river in the region of Mountain Altai. The name of the river is connected to Altaic word "kadyn" meaning "lady" or "mistress". Also, word "katun" means "a woman" if translated from Old Turkic.
Historical opinions about origins and the mystery of the family name of Katunin
"Katusha" is a derivative form of currently lost personal name "Katun", pedigree of which is unknown. In ancient Rus a baptismal name that sounded like "Katun" was used, which is now forgotten; "Katusha" was one of its derivative forms. It is not improbable, that the base of the name is word "katuna", meaning Muslims' slave wife. These are the possible origins of Katunin.
Katunin - During my long life I only met my namesakes three times; why is this last name so rare?
Speranskaya: The family name of Katunin derives from name "Katunya," a tender form of such names as old calendar name "Kat" and modern ecclesiastic names "Katun" and "Kutoniy". Name "Kat" derives from Latin word "catus" meaning "dexterous", "clever"; "Katun" derives from Roman family name "Katon"; "Kutoniy" derives from Greek word "kuphonus" meaning "light-winged" or "light-minded".