Nefesh, Ruach, and Neshama are states that we can reach and constantly stay in. The highest of them is Neshama. Therefore, this is the name of our spiritual part.
In addition, there are also states called Haya and Yechida. But these are supplemental, temporary additions to the state of the soul.
From KabYV’s “Fundamentals of Kabbalah,” 6/17/19