I really love this feature, but it gets confusing. I am not used to having dialogues with myself in game, and I reckon most other players will not have had that either. Therefore it is very important to have a very clear idea of who is talking when.
I think my main confusion comes from the portrait showing in the dialogue screen being for the previous person who spoke. If we could add another portrait next to the players response choices, showing who will be talking now, that would really help make things clearer and not slow the flow of the game as much for me.