It seems like the story presented is just a vehicle to explore the interactions of ettins and the ring of regeneration.
These interactions are edge cases not covered in the rules and are entirely up to the DM. There are multiple questions here:
- Can both heads of an ettin attune to the same item?
- Can the ring of regeneration regrow an ettin's head?
- Does a regrown head regrow its memories?
Can both heads of an ettin attune to the same item?
By RAW, seems at least possibly dubious.
The twin heads of an ettin are two individuals trapped in the same brutish body. Each head has its own mind, personality, and name, and possesses unique preferences and quirks.
I don't see that it's a given that they can attune to the same item.
But let's assume they can, because if they can't the other questions are moot.
Can the ring of regeneration regrow an ettin's head?
If we have assumed an ettin is one creature, and so both "individuals" are attuned to the ring, then regrowing the head seems reasonable:
If you lose a body part, the ring causes the missing part to regrow
So since the ettin has two heads, and it has lost one, it can regrow the lost one.
Does a regrown head regrow its memories?
D&D is not a biology simulator, and we left any reasonable biology behind at the first cantrip.
You can really argue either way:
- Yes, the memories grow back. The ring is magical, and it restores the head to "full functionality". One concern might be where do the restored memories get restored from? Of course, the obvious and perhaps only answer is "magic".
- No, the memories don't grow back. The head is restored as perfectly functional, but it has no memories. The ring makes no mention of regrowing any "customization" of the body part, such as tattoos or scars, so it does not regrow the memories. Of course, then the DM is faced with if memories don't grow back, is the regrown head basically mentally newly born? That might cause some interesting challenges for the surviving ettin.
So, DM's choice.
But really this is the wrong way around
It is up to the DM as to whether this is even an issue. It can be explored as an edge case in the rules, but unless a DM specifically wants to give an ettin a ring of regeneration, it doesn't happen.
And, if it does happen, then these answers are up to the DM. Maybe the DM wants the ring to work, maybe not.
But back to the ettin.
So there the PCs are. The ettin is lying dead, one head severed, and the remaining body, with second head attached.
Player 1: You fool. I told you the ring wouldn't regrow the head.
Player 2: Not my fault. We killed the other head before we could even find out.
Player 1: Now the continent is lost. Everything and everyone we love and know will be gone in a mere seven days. There's nothing we can do. It's hopeless. Everyone is doomed.
Player 2: Hey, look on the bright side. Now we have a ring of regeneration!
Player 3: Not to worry. We have speak with dead.
Player 4: Not to worry. We have create undead.
Player 5: Not to worry. We have resurrection.
Player 6: Not to worry. We have divine intervention.
Player 7: Not to worry. We have a ring of three wishes.
Player 8: Not to worry. A god owes us a favor.
Player 9: Not to worry. We know where the library of the gods is. I have a library card.
...
Player n: Not to worry. We have . . . .