Allow me to explain my question a bit. "KGB" is "Committee for State Security". But one of the founding principles of the Soviet Union is that everything would be governed by a council, or "soviet", instead of power being held by one person for too long.
Of course, we know that it never really worked out that way, but the Soviets were very good at talking the talk, as it were. Why, then, was the KGB named the "Committee for State Security" instead of the "Council(Soviet) of State Security"? Wouldn't it have made more sense politically for them to call it the Council of State Security?
The concept of the soviet (lower-case here to refer to the word itself) was a council (which indeed is what soviet translates to) of representatives of workers from factories. It was indeed the Petrograd Soviet (based in what is now St. Petersburg; name changed during the First World War to be less German-sounding) that ended up as the de facto parliament of the Provisional Russian government in 1917, and the body that helped bring the Bolsheviks to power in the October Revolution that year.
Now why soviets were not used to lead the various ministries of the USSR? Initially the very name of ministry was avoided, as Lenin wanted to avoid using a phrase that had imperialist and bourgeois connotations. It was Trotsky who came upon the idea of using the title "People's Commissariat," and so that was used (until 1946 when the phrase "Ministry" was adopted). Soviet was not used because at the head of the people's commissariats was a single individual, a "People's Commissar" (effectively minister), not a committee. However the collective body of people's commissars, what would be the cabinet, was indeed called a Council of People's Commissars, which in Russian was a Soviet (and indeed abbreviated, both in English and Russian, as the Sovnarkom, from the Russian Sovet Narodnikh Kommissarov).
Thus the NKVD, the predecessor to the KGB, as a Commissariat (the Commissariat of Internal Affairs), was given that abbreviation (from the Russian version of its name), it had its name changed to MGB (Ministry of State Security) in 1946 when, as noted above, the Commissariats were renamed ministries, and acquired the acronym KGB in 1954 when it was dis-attached from the Ministry of Internal Affairs (Lavrenti Beria had merged the two a few years prior), and no longer given a ministerial level.