My interpretation of your post is that you're both unfamiliar with the Naval Org tab and you want to create something believably Soviet to reflect the continuation of your game.
The ideal naval org tab is something useful for deployment visualization and reorganization. While retaining and reflecting the flavor you want to give your navy is important too, keeping your mind's eye on the first will save you many headaches.
I have found that there are essentially four activities for ships.
*Deployment - Squadrons actively deployed away from home. Typically includes pickets and ships permanently assigned to secondary bases.
*Reserves - All ships at home base. Although this can be further divided into the ready reserve and ships undergoing overhaul, I find moving things around in reserves on that basis to be a waste of time. Ships in the reserves are usually all in the same task group, making their status easy to see at a glance. The Naval Org tab lets you split squadrons out of the reserve quickly and easily.
*Working up - Ships with incomplete squadrons or that are undergoing TF training. Once training and initial overhaul is completed, they are assigned to reserves.
*Expeditionary - Major long range expeditions such as war fleets or groups attempting to confront distant Spoiler threats.
Over time, I've rejected putting civilian auxiliaries (cargo ships, colony ships etc.) into TFs, mainly it's a pain with minimal benefits. However, it's very helpful to have naval auxiliaries like fuel tankers and troop transports in the tab.
Finally... naming your task groups properly is important to making things easier. In my ideal, all similar squadrons are next to eachother in the Task Group dropdown. To accomplish this, I named my squadrons things like 'Division Battle 105' or Division Missile 207. Another method is to use abbreviations at the start of TG names - a riff on my earlier TGs would be 'DB105 Hyperion' or 'DM207 Tornado'.
I did some basic Wiki research and came up with the following sample scheme.
-Soviet Military Star Fleet (TF HQ)
--Solar Fleet
---BG 1st Operational Squadron
----NVG 5th Attack Group (Battle Squadron)
----NVG 6th Attack Group
----NVG 2nd Aviation Group (Aviation Cruisers)
----NVS 157th Star Regiment (Fighters)
--Centauri Fleet
---BG 2nd Operational Squadron
----NVG 3rd Attack Group
--Earth Military District
---SRF 43rd Rocket Army (Earth PDCs)
----NVS 124th Star Regiment
---SRF 27th Guards Rocket Army (Earth Defence Stations)
--Mars Military District
---SRF 30th Rocket Army (Mars PDCs)
--Military Reserves
---NVG 4th Attack Group
---NVG 1st Attack Group
---NVU Military Transport Command (Troop Transports)
--Training Command
---NVG 7th Attack Group
---NVS 43rd Star Regiment
---NVS 85th Star Regiment
---NVG 3rd Aviation Group
etc.
