The correct answer is option 3, 1969. The name of Madras State was changed to Tamil Nadu in 1969.

Option 1, 1956, is incorrect because this was the year when Madras State was initially formed after the reorganization of states based on linguistic lines.

Option 2, 1968, is incorrect because the name change occurred later than this year.

Option 4, 1967, is incorrect as well because the name change took place after this year.

It is important to note that the name change was a significant step in recognizing and acknowledging the Tamil identity of the state. It reflected the aspirations of the people and their desire for self-empowerment and cultural recognition.