Attaining a calm mind During the last 5 months I made observation regarding my inner mind process. The inner chatter which most people know during their day disappeared completely in my mind.
I practiced mindfullnes during my day and meditated as well. Is their a specific term in Buddhism which refers to achieving a quite or calm mind?
One could call it jhāna or dhyāna which is the meditation with a calm mind. You are on a great path. Perhaps you want to meditate on the heart sutra where it says:

"No suffering, no origination,
no stopping, no path, no cognition,
also no attainment with nothing to attain. "

The moment where you recognize a calm mind (the absence of something) as achievement, the ego crawls back up and claims having attained something. The true you is just about to get this ego to quite down. As you begin to research terms and more about having attained this great achievement you might create artificial distance again. Always remember that you are neither the mind nor the body.