I have 10/3 NM-B wire I am extending with 8awg THHN blk, red, grn. For the green, should I attach to the bare copper or insulated white and redesignate it as green? Since both are grounded at the CB panel, I'd like to use insulated to insulated if this would be permissable.
No, you may not.
The insulated white wire you are proposing to reuse as ground, is the neutral wire in a 240/120V circuit. (This causes some confusion because it is referred to in the NEC as a grounded conductor, and is bonded to the earth ground at the main service.) It is, for all intents and purposes, a normal current-carrying conductor and has to be colored white or grey. No other colors are permitted. (In sizes #4 AWG and larger it can be black with white tape, but that is irrelevant here).
The bare conductor in your 10/3 cable is the ground (referred to as equipment ground, earth ground, or simply grounding conductor). As such, it is only designed to carry fault current for short periods of time. The point of that wire is to trip a breaker should there be any fault in the circuit or connected equipment. It has to be green, green/yellow, or uninsulated - no other colors are permitted.
You are not allowed to redesignate a neutral as a ground. Your green wire should connect to the bare grounding conductor when you splice. The white conductor should be abandoned in place (and capped off with a wirenut in case you want to convert that back to a 240/120V circuit in the future).
You are making your splice in an approved accessible junction box with the THHN in conduit, correct? Better yet, if your boxes and conduit are EMT, then they become the grounding conductor and you can save that green THHN to make reusable ties for your plants.
Only certain wire re-marking is allowed.
Wires #6 or smaller, the only re-marking possible is a white wire being re-marked to be used as a hot, and even then, only if the wires are inside a cable. All other possible remarkings (all 5 combinations) are prohibited.
Except that a permanent conversion to ground may be made on any wire, by destroying all wire insulation that is reachable without opening up more of the cable sheath.
Wires #4 or larger, any remarking is allowed, except that if they start with a green sheath, they can't be remarked. Almost all wires that size are black anyway.
Since both are grounded at the CB panel
Yes, many people observe that and then leap to the wrong conclusion. You're seeing a illusion. The systems are totally separate except for a neutral-ground equipotential bond at the main panel. The equipotential bond could be anything that keeps neutral near ground voltage, however they chose "a piece of wire" because it is cheaper.
Now that you have 2 isolated bars right next to each other with a connecting wire, builders said "hey, why do we need 2 bars? Since they're connected anyway can't grounds just be guests on the neutral bar? It would be cheaper." And NFPA said "okay".
But they are still separate systems. They're only on the same bar because that's the main disconnect location.
I'd like to use insulated to insulated if this would be permissable.
Ever hear of the copper age? It's when humans first started manipulating metal. Why copper?
The vast majority of metals are found in nature only in oxide form. They "rusted". People were able to develop industrial processes to reduce them back to metal, but that wasn't easy so they didn't start there. Now a very few metals are very stable and have not oxidized for the 5 billion year history of this planet - they can be found in metallic nugget form, where they are instantly recognizable as metals. Gold and copper are two of them, that's why metalwork started there.
This thing was not kept in a climate-controlled museum for 5000 years.
So you see, your preference to have insulated wire doesn't make a lot of sense. If your environment is hostile enough to degrade copper, you have to take special precautions to deal with that.
Speaking of environmental problems, NM cable is not allowed outdoors. It quickly degrades.
Regardless, since you are extending hot-hot-ground with THHN, in conduit, and someone might hypothetically extend neutral in the future, you might want to reserve neutral for neutral.