I'm not sure if you're looking for a name for the "process" (I'm not aware of one) or an explanation of it.
The debate over whether personality is more greatly influenced by genetics or environment is often referred to as the Nature Vs. Nurture debate. Is that what you're looking for?
Well, I'm not certain I'm grasping your meaning, but I have an answer: Behavior Genetics. This is the name for the field that seeks to explain the role of both genetics and behavior on human psychological development.