Agreed, and a lot of the disputes in this realm come from people drawing identity in different ways. I submit that I am the entire system called "Thom Blake" as well as a bunch of other stuff like my smartphone and car.

Once you give up Platonic identity (or the immortal soul) you also get to have much fuzzier boundaries. A dualist who thinks "I am my mind" cannot imagine losing a part of oneself without "no longer being me", and thinks that cutting off one's hand has no impact on "who I really am". I think that cutting off my hand will have a great impact on me, in terms of my self and my identity, and cutting off my right hand less so than my left.