I put the encyclopedia back, and I didn't think to check on how many popes took the name of the prior pope. John Paul I was the first to draw on the two previous popes, and then, of course, John Paul II decided to honor the September pope.
TS
It seems that there's been no real single standard throughout history for "pontifical onomastics" (e.g. the reasoning behind papal names.) Motives have ranged from honoring those who have helped a new pope, to recalling those who have helped the new popes' families, or even to reinforcing "political interests".
This last motive can be seen most prominently during the Great Schism when the Roman Pope-names recalled prior Roman names, and the Avignon Popes chose the names of Popes partial to France.
In an article by Bernd-Ulrich Hergemöller for "The Papacy: An Encyclopedia", we find the following regarding "recent" Popes:
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From the 16th century, the name chosen has invariably been inspired by the principle of pietas: PAUL IV, GREGORY XIV, CLEMENT X, INNOCENT XI, INNOCENT XII, CLEMENT XII, CLEMENT XIII, BENEDICT XIV, CLEMENT XIV, PIUS VII, PIUS VIII, and PIUS XII took the names of those predecessors who had raised them to the cardinalate.
JULIUS III, PAUL V, and GREGORY XV chose the name of the pope who had launched them on their curial CAREER.
CLEMENT VIII, LEO XI, INNOCENT X, ALEXANDER VII, and INNOCENT XIII chose the name of the pope who had actively supported their family.
PAUL IV, PIUS V, SIXTUS V, and ALEXANDER VIII adopted the names of those predecessors whose nephews had contributed to their election.
Taking a predecessor’s name not only was a way of giving symbolic thanks but also implied the wish to be faithful to a spiritual heritage. Hence the stereotypical, conservative character of pontifical names in the modern era. Julius, Marcellus, and Sixtus were chosen once; as for the others, the choice of names over the roughly four centuries from the council of TRENT to VATICAN II boils down to nine: Paul, Pius, Gregory, Urban, Innocent, Clement, Leo, Alexander, and Benedict. In the 17th and 18th centuries, the name Clement takes the lead, and then, until 1958, the name Pius.
John XXIII (A. Roncalli, 1958) was the first to take the name of a medieval pope, thus symbolically emphasizing the end of the “papacy of the Piuses.” His successor PAUL VI’s choice was a subjective one, inspired primarily by a theological consideration. John Paul I was the first pope in history to adopt a double name, but his choice still obeyed the principle of respectful pietas toward his predecessors. The pontifical name of JOHN PAUL II invokes the memory of his three immediate predecessors.