1) Pius. There is a huge effort within the church to revive the memory of Pope Pius XII, who saved hundreds of thousands of innocent lives during the Holocaust (For those upset that he didn't make a lot of public statements condemning the Nazis, understand this: The Germans informed him that if he said anything, they would kill 400,000 Jews as a result. So instead, he ordered monks and nuns to open their doors to refugees, establishing an underground network throughout the city of Rome.) Many cardinals recognize this, and so a Pius XIII is the most likely name for the next pope.
2) Gregory. This one hasn't been used since the 19th Century. Considering the other options, this one might just be chosen.
3) John. Since Pope John XXIII is still quite popular, and is remembered as a smiling and humble man, a cardinal choosing his name would send a signal that he wants to connect with people, and is "one of us". However, the next Bishop of Rome may not want to eclipse John XXIII, and will probably choose a different name.
Other possibilities include a John Paul III, Paul VII, or Clement XV. But he may decide to do an unconventional name (Perhaps Joseph, Matthew, Luke, or something completely different, like John Benedict.) Thoughts?
Oh, and for non-Catholics reading this, please: No Trolling.