How to make sure a player will not draw their own character card as target?
A game with a similar mechanic is Lifeboat. In that game normally you get points if your target dies, but if your target is yourself then instead you are a "psychopath" and get points for anyone who dies (but fewer points in other ways).

One solution for your setup could be to put both player ID and target on a single card: "You are player 1; kill player 2", "You are player 2; kill player 3", through "You are player n; kill player 1".