Pope John XXIII called for the council and opened it. However, he died before it ended and it was closed by Pope Paul VI.
As of 30 May 2014 there have been two named saints from the Second Vatican Council. Pope St. John XXIII was the pope that called the Council, and Pope St. John Paul II was a participant in the Council.
Pope John XXIII
Pope Paul III called for the council.
Pope Pius IX convened the First Vatican Council which began in 1868. Pope John XXIII convened the Second Vatican Council which began in 1962. Pope Paul VI reconvened the Second Vatican Council in 1963 after it was suspended due to the death of Pope John. Pope John had to close the First Vatican Council before opening the Second Council since the First Council was never officially closed by Pius, it ended abruptly, or temporarily suspended because the Franco-Prussian War broke out and the bishops in attendance wanted to return to their diocese. After Rome was captured, Pope Pius permanently suspended the Council but did not close it officially. Pope John died during the intermission break between the first and second session of the Second Council to which it was suspended. Once Cardinal Giovanni Montini was elected as Pope Paul VI, he reconvened the Second Council and presided over it until its ending in 1965.
Pope Paul VI
Pope John XXIII called for the council and Pope Paul VI continued it after he was elected pope in 1963.
Pope John XXIII called the council and Pope Paul VI continued it in his reign.
Pope Paul VI closed Vatican II.
Pope John XXIII convened the Council and Pope Paul VI made the changes to the Mass.
Pope John XXIII called the council.
Pope Pius V called for the First Vatican Council.
No, Pope Urban II called the council.