Yes, I know I am using NATO designations for the Russian missiles. I've always done that in previous campaigns as well. I guess it's because I grew up learning about Soviet warships from a Western perspective and the NATO designation seems a lot more familiar.
Off course, USSR designation most difficult and confused than NATO. It happened due to espionage paranoia existed in the leadership of the USSR. But, IMHO, using soviet/russia designation gives more authenticity to the story.
I use in most my campaign for Russia missile next designation -
P-x000 for shipbased antiship missile. Name for missile type - rocks e. g. Granite, Basalte, Malachite, Onix. (for example P-1000 Basalte or P-2000 Hematite)
Kh-xxx for fighterbased antiship missile. (for example Kh-200 or Kh-201)
R-1xx for antimissile (for example R-121 or R-100)
R-xx for space analog ICBM (powerful warheads and long range - hundreds of millions or billions of kilometers) (for example R-10 Bulava (at English - mace) or R-11 Sineva (Azure)). I did not see any tradition in naming for the ICBM in the Soviet Union or Russia. I just use an already used names.
Sorry for my English. I have bad English grammar, so sometimes errors can occur.