Our name is our soul, our Nefesh. It is also sometimes referred to as Yisrael in general. (Ohr HaHayyim on Parashath Pinhas)
Our name is unique (and relates) to the combination of Nefesh(soul) Ruach(spirit) Neshamah(breath) that we have. (Hesed l'Avraham 5:2)
I imagine they agree and the Ohr HaHayyim was talking more generally. They definitely both agree (and mention) that our negative actions obliterate our name. (שם רשעים ירקב - a villain's name will rot)
Think about this, your name is more you than your body.
When we talk about creation both at the beginning and the end, we mention God and His Name. (existing, and being One (indivisible))
You have a name too. That's the divine image in which you were created. When it is guarded intact, angels, animals, and all of creation are in awe of you.
Use it well.