What even is "personality" - leaving aside technical and dictionary definitions, if you --the person-- are the sum of your life experiences, can you ever truly not be you? I pose this because I encounter resistance from people to the notion that they can change themselves, lest they lose some notion of their "self", and personality is often equated with "self" from my experience.
To say that making someone less "neurotic" changes their personality is about like saying giving someone a prosthetic leg which allows them to walk again changes their personality. It may certainly change the kinds of things they do on a regular basis, but it didn't change the basic concept of self we commonly think of as "personality".