Despite all of the Soviet hardware having designations already, many systems were given different names by NATO. For example, the 9K37 Buk was called the SA-11 "Gadfly".
But not all systems - seemingly AFVs tend to use the native designation even in the West - T55, BMP-2, BTR-60.
Why the parallel system? Why for some things and not others? How were the NATO codenames chosen?
First time responding here. So, hopefully I get this right.
Basically it has to do with creating a standardized system that allows for the easy and clear communication between NATO allies about Russian forces. Each type of weapon system is given a letter designation. F, for fighter, C, for cargo aircraft, T for tank, etc. Using your example, the SA-11 Gadfly is a surface-to-air missile. All SAMs were given names that began with G.
Without the system you might possibly have this scenario: NATO and the Warsaw Pact are at war. You and I looking over a map with the latest intelligence on Russian positions and force composition in order to plan our next offensive in southern Germany. You look on the map and see 9K37 Buk and remember from some brief that that is a SAM missile and thus NATO will have to be careful in using air assets in that area. I on the other hand, sort of kindof not really remember that same brief and actually think the 9k37 Buk is a Soviet artillery unit. In all the commotion of planning, we forget to confirm this as we put together our plan of attack. With our plan ready, you go off to communicate to NATO ground forces our plan, I on the other hand go off to communicate with our NATO air assets our plan. I fail to inform our air assets of the SAM missiles in the area because I still think they are artillery units. As a result, the air assets that are supposed to cover our offensive go in without neutralizing the SAMs and as a result take heavy causilities leaving the ground forces without air cover.
However, with standard NATO designations, as we look over the intelligence, you and I both see Gadfly and instantly know that that unit is a Soviet SAM unit. I may not know specifically which one, but I am now alerted to the fact that the area we are planning to assault has air defense units in the area and will require additional planning and research to ensure a successful assault.
Here is a website that gives some information on the designation systems (is specfically for aircraft and missiles): NATO Designations
Giving foreign equipment reporting names that are easier to remember and pronounce didn't start with the Soviets. E.g. the U.S. military had given every japanese warplane its own nickname in WW2. "Zero" for the Mitsubishi A6M fighter, "Kate" for a type of bomber etc. It also happened with german equipment. To this day, many americans refer to the Panzerkampfwagen IV as "Mark 4". And giving your own equipment official nicknames has been standard practice for just as long.