The part of the brain associated with thinking and language is sometimes called the brain.

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The right answer is "Rational" brain. This alludes to the Cerebral Cortex, whose responsibilities are: the processes of thought, perception and memory as well as the progressive motor function, social abilities, language, and problem solving. This is a  thin mantle of gray matter. Its size is like the one of a formal dinner napkin casing the surface of each cerebral hemisphere. It is wrinkled and folded, creating numerous convolutions (gyri) and crevices (sulci). It is made up of six layers of nerve cells and the nerve pathways that link them.