what if the twin died and for some reason the mc replaced them and that is why there was a option to choose their name (i think that would be cool asf but i don't really think that makes sense. also if one of them would replace the other, the replaced would clearly be the mc)
I mean honestly I just thought of the "generic" her sister was sent to a asylum or that cliché where the whole family died in a car accident on rainy day.... But to add onto your thoughts, what if the voice is the sister? Our mc clearly had a strong reaction to that one incident so maybe something happened in the future(killing the parents maybe? or someone or something else) which caused our mc to do the deed and this is how they cope and its probably why they are a "vigilante" killing people they deem "bad".
Actually your idea reminds me of the game "Martha is dead" with the whole twin replacing the dead twin thing.