These are the list of all the possible regnal names (may not be entirely complete, since I may miss some in the way), that the new Pope can and may take as his own regnal name. In parentheses are how the name will look like if the Pope takes the name.
The ones listed below are the names that Popes had been taking since 1775 till today (2013) :
1. Benedict (Benedict XVII) last Benedict still living as Pope Emeritus
2. John Paul (John Paul III) last John Paul died in 2005
3. Paul (Paul VII) last Paul died in 1978
4. John (John XXIV) last John died in 1963, no John before that since 1334
5. Pius (Pius XIII) last Pius died in 1958
6. Leo (Leo XIV) last Leo died in 1903
7. Gregory (Gregory XVII) last Gregory died in 1846
Below are the names that the Popes had taken before 1775, but this does not rule them out from being picked by the new Pope, but chances are remote, with the above 7 names in use for the past 238 years.
8. Clement (Clement XV) last Clement died in1775
9. Innocent (Innocent XIV) last Innocent died in 1724
10. Alexander (Alexander IX) last Alexander died in 1691
11. Urban (Urban IX) last Urban died in 1644
12. Sixtus (Sixtus VI) last Sixtus died in 1590
13. Marcellus (Marcellus III) last Marcellus died in 1555
14. Julius (Julius IV) last Julius died in 1555
15. Adrian (Adrian VII) last Adrian died in 1523, last non-Italian Pope before 1978
16. Callixtus (Callixtus IV) last Callixtus died in 1458
17. Nicholas (Nicholas VI) last Nicholas died in 1455
18. Eugene (Eugene V) last Eugene died in 1447
19. Martin (Martin VI) last Martin died in 1431
20. Boniface (Boniface X) last Boniface died in 1404
21. Celestine (Celestine VI) last Celestine died in 1294, also a Saint, the famous Pope who resigned
22. Honorius (Honorius V) last Honorius died in 1287
23. Lucius (Lucius IV) last Lucius died in 1185
24. Anastasius (Anastasius V) last Anastasius died in 1154
25. Eugene (Eugene IV) last Eugene died in 1153
26. Gelasius (Gelasius III) last Gelasius died in 1119
27. Paschal (Paschal III) last Paschal died in 1118
28. Victor (Victor IV) last Victor died in 1087
29. Stephen (Stephen X) last Stephen died in 1058
30. Damasus (Damasus III) last Damasus died in 1048
31. Sylvester (Sylvester IV) last Sylvester died in 1045
32. Sergius (Sergius V) last Sergius died in 1012
33. Agapetus (Agapetus III) last Agapetus died in 955
34. Marinus (Marinus III) last Marinus died in 946
35. Lando/Landus (Landus II) only used once, died in 914, last Pope whose name is only used once
36. Theodore (Theodore III) last Theodore died in 897
37. Romanus (Romanus II) only used once, died in 897
38. Formosus (Formosus II) only used once, died in 896
39. Valentine (Valentine II) only used once, died in 827
40. Zachary (Zachary II) only used once, died in 752
41. Constantine (Constantine II) only used once, died in 715
42. Sisinnius (Sisinnius II) only used once, died in 708
43. Conon (Conon II) only used once, died in 687
44. Agatho (Agatho II) only used once, last one is Saint, died in 681
45. Donus (Donus II) only used once, last one died in 678
46. Adeodatus (Adeodatus III) last Adeodatus died in 676
47. Vitalian (Vitalian II) only used once, died in 672
48. Severinus (Severinus II) only used once, died in 640
49. Sabinian (Sabinian II) only used once, died in 606
50. Pelagius (Pelagius III) last Pelagius died in 590
51. Vigilius (Vigilius II) only used once, died in 555
52. Silverius (Silverius II) only used once, last one is Saint, died in 537
53. Felix (Felix V) last Felix died in 530
All the names below have been used only once, ever. Most of them are the early Church Fathers and Saints, and therefore, it is rather extremely unlikely any of these names would be picked.
54. Hormisdas (Hormisdas II) only used once, died in 523
55. Symmachus (Symmachus II) only used once, last one is Saint, died in 514
56. Simplicius (Simplicius II) only used once, last one is Saint, died in 483
57. Hilarius (Hilarius II) only used once, last one is Saint, died in 468
58. Zosimus (Zosimus II) only used once, last one is Saint, died in 418
59. Siricius (Siricius II) only used once, last one is Saint, died in 399
60. Liberius (Liberius II) only used once, died in 366
61. Mark (Mark II) only used once, last one is Saint, died in 336
62. Miltiades (Miltiades II) only used once, last one is Saint, died in 314, First Pope after Edict of Milan
63. Eusebius (Eusebius II) only used once, last one is Saint, died in 310
64. Marcellinus (Marcellinus II) only used once, last one is Saint, died in 304
65. Caius (Caius II) only used once, last one is Saint, died in 296
66. Eutychian (Eutychian II) only used once, last one is Saint, died in 283
67. Dionysius (Dionysius II) only used once, last one is Saint, died in 268
68. Cornelius (Cornelius II) only used once, last one is Saint, died in 253
69. Fabian (Fabian II) only used once, last one is Saint, died in 250
70. Anterus (Anterus II) only used once, last one is Saint, died in 236
71. Pontian (Pontian II) only used once, last one is Saint, died in 235
72. Zephyrinus (Zephyrinus II) only used once, last one is Saint, died in 217
73. Eleuterus (Eleuterus II) only used once, last one is Saint, died in 189
74. Soter (Soter II) only used once, last one is Saint, died in 174 or 175
75. Anicetus (Anicetus II) only used once, last one is Saint, died in 166
76. Hyginus (Hyginus II) only used once, last one is Saint, died in 140 or 142
77. Telesphorus (Telesphorus II) only used once, last one is Saint, died in 136 or 138
78. Evaristus (Evaristus II) only used once, last one is Saint, died in 105 or 107
79. Anacletus (Anacletus II) only used once, last one is Saint, died in 88 or 92
80. Linus (Linus II) only used once, last one is Saint, died in 76 or 79
81. Peter (Peter II) only used once, and he is the founder of the Church, Apostle of Jesus Christ, and it is extremely unlikely any future Pope, or any Pope will ever adopt the name of the Prince of the Apostles.
petercanisiusmichaeldavidkang 