If he can use two names, why not three? Pope Jean-Paul Sartre I! The first existentialist pope! And he should also be an unshaven chain-smoker, just for effect! 
After reading the “Malachy prophecies” stuff (see my MPSIMS thread for links on this):
“They call him G - L - O…”
:: ducks and runs as Tom~ pursues me with bell, book, and candle ::
smack
That one actually made me cringe…
Pope Shlomo I
Someone on Google Answers quotes a helpful extract from an article by Bernd-Ulrich Hergemöller in 'The Papacy: An Encyclopedia":
"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."
Mr. Blue Sky:
You’re thinking of Rio, by Duran Duran.
So if I understand that extract correctly Aldiboronti, my idea about a Pope Leo are out the window and we are more likely to get John XXIV, Paul VII, or John Paul III. Hmmmmm. But if whoever gets the post wants to reach further back doesn’t that seem that Leo could be a logical choice?
I understand the sentiments behind a tradition of names, but when you’ve got something like twenty five Johns or Peters or whoever, it makes me wish they’d each pick a unique name. “That’ was John the 17th.” “Uhh, cite? I think it was the 18th.” “No, no, you’re both wrong it was the 15th! C’mon, the 18th was a hundred years later! Get your popes straight!”
You gotta wonder, how many guys going into the conclave will be thinking of the name they will reign under, if they are elected.
How about Alexander IX? In honor of Alexander VI, the Borgia pope who hosted huge orgies in the Vatican! Let the good times roll!
Of course, if new pope is at a loss re his new name, he can always consult the Great Queen Spider! 
Based on current naming trends, the next Pope will most likely be named Jacob if a boy or Emma (Emily) if a girl. (Personally I would like for him to be Adrian V just to worry those who associate the name with the antichrist from Rosemary’s Baby, but Madison and Connor are also nice.)
No, that’s the name of the Pope 60-odd years hence. 
All hail Pope Connor I. :rolleyes:
Pope Sidious?
I hope it’s not John Paul III-I think that would be a mistake.
Sad but true. In the two thousand years of church history, there were occasionally problems with the enumeration of the Popes. For example, there was never a John XX.
Or Snoop Popey Pope. And he should have big ass spinners on the Popemobile.
Well, as long as they reunited The Shadows of Night, (or resurrected Jimi) to make the announcement. I don’t want any lassie-come-lately pop diva introducing the new pope.
(Of course, if they could bring Jimi back for the announcement, they could call the next pope Joe.)
Wasn’t one of the Innocents the pope Dante had in hell in his Inferno? If I’m remembering correctly, I doubt the next guy will choose that name.
I’m hoping for something new - Leo, Gregory, or Benedict fits that nicely. But I’m not Catholic, so what do I know?
“Onarope I” made me laugh out loud.
[monty python]
Look, when yer Bishop of Rome, ye’ve got more important things to do than remember yer bloody number!
[/mp]
I think that was Innocent V, whom Dante felt was a heretic. Of course, whether or not he was had more to do with whether you were a Guelph or a Ghibelline (to put things in black and white, so to speak.) Dante’s opinion didn’t discourage the name, though; there were a number of Innocents after him. They went up to Innocent XI, at least.
I like the idea of John XX, because that gap just bothers me. Worse, there already was a John XXIII before 1958, though the original John XXIII was an antipope. What’s the big deal? I don’t think George W. Bush was legitimately elected in 2000, but I still say he became the 43rd president in 2001. It’s the same thing! John XXIII should have been John XXIV But they won’t listen. They never do. “It’s been six hundred years! Let it go!” they’ll say. “It’s just a number!” they’ll say. Yeah, well… yeah, yeah…
I vote for Alexander IX, because the original Alexanders go so far back in history that choosing such a name would send no kind of signal of continuity. I have a hunch that the Vatican wants to change direction, so a name with no baggage would be ideal. I like the idea of Francis I; it is odd that no one ever chose that name before.
I’d love to see a pope with the chutzpah to call himself Peter II, but others have provided plenty of reasons why that probably won’t happen. Or how 'bout Celestine VI? There’s a signal for you! Time for some mystic crystal revelations!