I put up the German word for pope names into Google and the first site that came up already gives a good explanation of why they change their names: the first -according to the text of
www.kath.de/kurs/vatican/papstnamen.php- few popes did so to get rid of their unchristian, ie. heathen or politically charged or quite vulgar names. Later on the change of name symbolled the new dignity and also meant to show that the pope, i.e. the person who continues the work of St. Peter, has become a "new person".
And no one else but St. Peter changed his name first. He was Simon, called "Kephas", the rock, by Jesus himself (rock, Greek petros, I think... erm. My Greek is positively non-existent).
The commonest pope names have become John, Gregor, Benedict, Clemens, Leo, Innocence (spelt like that in English?), Pius, Boniface, Alexander, Paul, Nicholas and Martin (so the text also says). The first John Paul also was the first to choose a double name, followed by the recently deceased John Paul II - both meaning to thus honour their predecessors John XXIII and Paul VI.