Does our basic personality remain throughout every lifetime?

The personality can change depending on the parents you chose.  In most cases it normally remains very similar as the soul usually looks for parents that will have a compatible DNA encoding.  It can also be determined by the life lessons that the soul is working on.  The wisdom gained is always carried with the soul and remains constant.  Whether the soul awakens to it so it can be accessed all depends on the personality and events in their life.  The personality can be determined by the wisdom gained as well as the DNA.