(Redundant material deleted after the Great NATO Codename Merge of 2001.)

By the way, Tu-160 is Blackjack, not Bear (Tu-95 or Tu-142). Archer is AA-11, and Atoll is AA-2.

Most NATO codenames for Russian submarine types are based on the military radio phonetic alphabet; thus Whiskey, Tango, and Foxtrot are all Russian submarine classes. These seem to have been assigned randomly; both the Zulu and Foxtrot classes date to the 1950s, for example, while Alfa and Hotel date from the 1970s, so they aren't chronologically assigned.

After running out of phonetic alphabet entries in 1985, NATO switched to another alphabetical sequence, this time being allocated in order, and based on Russian-fish themes: Akula and Beluga being the first two assigned. There are a few exceptions to this scheme; for example, the Typhoon class ballistic missile sub was named after Leonid Brezhnev referred to it as 'Tayfun' in a speech; that name appears to have been dropped on their end, but stuck in NATO usage. To add to the confusion, the Typhoon is known to Russia as the Akula class, but is a different type from what NATO calls Akula.

NATO started out using Russian words beginning with 'K' to designate classes of surface ships, but has generally switched to naming the class after the first ship of the class built, for example, the Slava class guided missile cruiser. Again, this can be confusing; many types started out with a temporary reporting name (Slava's was originally "Black-Com-1" for Black Sea, Combatant, Type 1), then were assigned a K-series reporting name (Slava's being "Krasina"), then were later referred to by their real class name (which in more than one case coincidentally started with a 'K', such as the type codenamed Kurile, which turned out to be the Kiev class!).

Probably the worst naming confusion in the Russian surface fleet surrounds their full-deck carrier, the first example of which was renamed by the Russians at least once during construction. This class is variously known as Black-Com-2, Kremlin, Tbilisi, Brezhnev, and Admiral Kuznetsov.

Despite the intelligence community convention of putting reporting names in all caps, I'll be using mixed-case names in my writeups to avoid the implication that they might be acronyms. Like many geeks, when faced with a series of capital letters, I tend to start a computationally-intensive acronym-expansion background process to figure out what's being talked about.
The previous writeup I had here was severely wrong. I'm indebted to Andreas Gehrs-Pahl's excellent military technology site at http://www.ais.org/~schnars/aero/index.htm for more accurate information.