Another word/way to describe "Core Self"

Solution 1:

You could say true self, the definition according to MW1:

the type of person one really is

Example sentences (from OLD2, under more example sentences for point 1):

‘He understood me and I didn't have to hide my true self from him.’2

‘Where you expect to find your true inner self, you will come face-to-face with a mob of strangers.’2

‘Now I gently introduce others to their intuition and often their true selves.’2

Another, perhaps even more suited word is inner self, definition according to CD:

a person's true or internal mind, soul, or nature3

Example sentence:

'a quest to find your inner self and your own uniqueness'3