In the beginning of the game, after you make a contract and have a blood transfusion, you have a nightmare about a beast arising from the blood, the beast approaches and as it reaches out to you in a gesture of wanting you to accept it, it bursts into flames upon touching you. I’m guessing this is a metaphor for you’re immune to the rampant beasthood curse plaguing the town and it’s for this very reason the messagers came for you. They see your immunity as a sign that you’re some sort of super hunter and so brand you with the mark of the hunter. Hence why the doll says soon after, “Ah, you found yourself a hunter.” In consequence, you’re robbed of your memories and somehow infused with fighting skills...or maybe you always had them? Clearly you’ve been indentured into the dream hunters by the messagers.
It’s really all a hypothesis but it’s how I make sense of it.