Self-reflection? Mindfulness? How to call such a cognitive process of a person, who often keeps monitoring his or her behaviour by asking oneself questions like "why you are doing it" or "what do you really want to attain", someone who investigates the real causes of his/her behaviour, even if it's painful and requires to face defence mechanisms? I thought it was a ''self-reflection'' or a ''mindfulness''... but I'm not sure [Please don't give me a link to wikipedia, 'cause this article is not finished]. Thank you in advance :)

I ask this question in the context of doing some research or writing some popular science article or reviewing some science literature about it. It's easier to dig in Ebsco bases knowing which term is proper. I just don't want to end up confusing terms, like many laypeople do with "fear" and "neuroticism".
Self aware or introspection would probably be the a good way to describe it.

Here is a non wikipedia link which gives a detailed explanation of interospection

You could also say self conscious but that is sometimes associated with a negative emotion.