Can a pope name his successor? Is it possible for a pope name his successor?

There are some that believed that the Prince of the Apostles, St Peter, actually named his successor, but this tradition can in no way be verified. There is also some disagreement that St Linus may not have been his first successor.


  All the ancient records of the Roman bishops which have been handed down to us by St. Irenaeus, Julius Africanus, St. Hippolytus, Eusebius, also the Liberian catalogue of 354, place the name of Linus directly after that of the Prince of the Apostles, St. Peter. These records are traced back to a list of the Roman bishops which existed in the time of Pope Eleutherus (about 174-189), when Irenaeus wrote his book “Adversus haereses”. As opposed to this testimony, we cannot accept as more reliable Tertullian’s assertion, which unquestionably places St. Clement (De praescriptione, xxii) after the Apostle Peter, as was also done later by other Latin scholars (Jerome, Illustrious Men 15). The Roman list in Irenaeus has undoubtedly greater claims to historical authority. This author claims that Pope Linus is the Linus mentioned by St. Paul in his 2 Timothy 4:21. The passage by Irenaeus (Against Heresies III.3.3) reads:
  
  After the Holy Apostles (Peter and Paul) had founded and set the Church in order (in Rome) they gave over the exercise of the episcopal office to Linus. The same Linus is mentioned by St. Paul in his Epistle to Timothy. His successor was Anacletus.
  
  We cannot be positive whether this identification of the pope as being the Linus mentioned in 2 Timothy 4:21 goes back to an ancient and reliable source, or originated later on account of the similarity of the name. - Pope St. Linus (67-76)


Traditionally there have been three ways the College of Cardinals could elect a new pope: election by acclamation  quasi ex inspiratione, election per compromissum and election of the Roman Pontiff by secret ballot.  

In Pope John Paul's Apostolic Constitution UNIVERSI DOMINICI GREGIS, He suppressed the first two possible manners of electing a successor and the only way to elect a new pope is by secret ballot. 


  Finally, I have deemed it necessary to revise the form of the election itself in the light of the present-day needs of the Church and the usages of modern society. I have thus considered it fitting not to retain election by acclamation  quasi ex inspiratione, judging that it is no longer an apt means of interpreting the thought of an electoral college so great in number and so diverse in origin. It also appeared necessary to eliminate election per compromissum, not only because of the difficulty of the procedure, evident from the unwieldy accumulation of rules issued in the past, but also because by its very nature it tends to lessen the responsibility of the individual electors who, in this case, would not be required to express their choice personally.
  
  After careful reflection I have therefore decided that the only form by which the electors can manifest their vote in the election of the Roman Pontiff is by secret ballot.


No where is it mentioned that a pope may name his successor personally. Can a pope actually name his successor before he dies?
This has happened in early times, but is not something likely to happen now. Pope Felix IV nominated his successor, Boniface II, although his papacy was disputed by some of the Roman electors. Boniface, in turn sought to nominate his own successor, but withdrew after strong opposition.