Kostikov was connected to Department 13 of the First Chief Directorate (today's SVR).
A Kremlin-loyal triple agent, Soviet Embassy Security Officer Ivan Obyedkov, "volunteered" the radioactive name "Kostikov" to a forgetful Lee Harvey Oswald or "Oswald" over a sure-to-be-tapped-by-CIA phone line on 1/10/63.
The
only reason the CIA and the FBI believed on 23 November 1963 that KGB Colonel-diplomat Kostikov was Department 13 was because another Kremlin-loyal triple agent, KGB Major Aleksey Kulak (J. Edgar Hoover's shielded-from-CIA "Fedora" at the FBI's NYC field office), had told the FBI in 1962 that Kostikov's charge at the UN, Igor Brykin, was Department 13.
Kulak was the guy who tried to support false defector-in-place in Geneva in June 1962 / false (or perhaps rogue) physical defector to the US in February 1964 Yuri Nosnko's bona fides by "confirming" that he was a Lieutenant Colonel and that he had received a "return to KGB headquarters immediately" telegram in Geneva in late January or early February 1964, only to have to lamely retract those two "confirmations" when Nosenko later confessed during harsh (but non-tortuous) interrogation that he was only a "captain" and that he hadn't received said telegram.
Fun fact: Gerald Posner befriended Nosenko while writing "Case Closed" because Nosenko was telling him exactly what he wanted to hear -- that the KGB had absolutely nothing to do with "abnormal" former Marine sharpshooter and U-2 radar operator Oswald during the two-and-a-half years he lived in the USSR.
LOL!