It's unchanging. Personality is very subject to change; I used to be an arrogant bully, for example, caught up in his own little world, almost completely oblivious to the outside world. (This was primarily in Middle School.) Now, just barely a decade later, only a small vestige of that personality remains. (I still haven't quite figured out how to be fully "present.") The soul is, essentially, not subject to change.
Sure, from what I've heard (I'm too young to really know if this is true), once you become an adult, it's really hard to change personality. But, at the same time, I've heard of it happening, so the point still stands: personality is not what our true identities are.