If there's a name attached, report it. That's all you can do. If they're boneheaded enough to have their more personal info on their profile, then you can go further and possibly even contact authorities if you want to teach them some kind of lesson.
If it's anonymous, then there's literally nothing you can do. Except turn off anonymous messages, I guess. If hate mail bugs you that much, then that should be the first thing you do anyway. Won't stop it, but it'll stop the less determined trolls.
In either instance, if the person actually wanted to kill you, and they were able to find you and had the means to carry out the murder, then there is nothing you can do about it any more than what you can do about anyone else wishing they could kill you.
So, the best course of action is to just ignore it, because you cannot do anything otherwise. Unless you plan to tip toe through life because random schmuck #194023 online said they wish they could beat your face in.