There are a few sources we keep in mind when attempting to identify the names:
This is meant for the first series, Around the World with Willy Fog. Willy Fog 2 and will be documented another day
The episode is identified by the narrator as The Wager, which is consistent with BBC listings and earlier BRB uploads. BRB later changed the name to The Bet. Both are correct translations of the original Spanish title, La apuesta, although The Wager is generally considered the more correct title.
The narrator gives the title as Bon Voyage. The same title is also on the US Sony VHS cover. The BBC gives the title as The Departure, which is also used by BRB. Both Polish dubs use a translated version of Bon Voyage. Bon Voyage is, thus, assumed to be the title. No episode title is given in the preview in episode 1, with the narrator simply stating that "The excitement and adventure begin in our next episode, as we commence our thrilling journey Around the World with Willy Fog."
Both the preview and episode 3 itself name the episode The Mysterious Mademoiselle. The title also appears on the US VHS. BRB uses A Rough Trip, while BBC uses The Eventful Journey. Mademoiselle does however appear, translated, in the second Polish dub.
The episodes, the BBC and the VHS release identify it as The Temple of Doom, which is also used in the second Polish dub. BRB gives the title as Willy Fog Wanted, which isn't exactly representative of what the episode is about.
Likewise, both the episode and the BBC name this episode as The Counterfeit. The VHS calls it The Counterfeit Fog, while BRB names it Willy Fog and the Ghost.
The narrator calls it Bombay Adventure, consistent with the BBC. BRB calls it Adventure in the Pagoda. No VHS tape could be found, but according to copyright registrations, it also used the Bombay Adventure title.
The End of the Line is the title given by the episode itself, which is also used by the BBC, and translated in the second Polish dub. The first Polish dub and BRB, however, use The Express of Calcuta. No VHS tape could be found, but according to copyright registrations, it also used the End of the Line title.
The title is given as The Deadly Jungle in the episode, in the BBC, on the VHS tape and in both Polish dubs. BRB uses the similar Danger in the Jungle.
In a case of discontinuity in the episodes themselves, episode 9 gives the title The Remarkable Rescue of Romy, while the preview in episode 8 gives the title as simply The Rescue. The latter title is however more common; it is used by the BBC, and is translated in both Polish dubs. BRB calls it Romy's Rescue. Nevertheless, The Remarkable Rescue is the title given in episode 9, and is thus considered proper.
No title is given in both episode 10 and the preview in episode 9. The BBC uses the translated Spanish name A Present for Parsi, which is also used by BRB. The Polish dubs use a title that roughly translates to The Indian Princess. As no official title was ever given, the second-best choice, the BRB title, thus A Present for Parsi, is used.
Beginning a streak of pretty consistent titles, the episode and the BBC names it Guilty as Charged, while BRB names it Rigodon's Derby.
Likewise, the episode is called Shipwreck everywhere except BRB, which calls it Storm in the China Sea.
And again, The Butler's Dilemma is used in most places. BRB calls it Rigodon Swallows the Bait. The first Polish dub title translates to "The Treacherous Drink", which is more representative of what happens in the episode.
This is another episode for which no title is given in the episodes themselves. The BBC calls it En Route for Yokohama, while BRB calls it Yokohama Bound. The first Polish dub calls the episode Pirates. En Route is considered the correct title.
All known sources call the episode Akita's Circus. This leaves no doubt about the episode's title.
The episodes give it the title of Adventure in Hawaii. The BBC, meanwhile, titles it Hawaiian Party, while BRB calls it Holiday in Hawai [sic]. Wikipedia gives a slightly different title, Holiday on Hawai.
Another episode with no given title. The BBC calls it A Trip in a Balloon, BRB calls it Voyage in a Balloon, while Wikipedia gives the title as the gramatically incorrect Vollage Balloon.
A title of The Showdown is given by the narrator in the episode, and in the BBC. BRB calls it On the Pacific Railway.
Moment of Truth is given by the narrator. The same title is used by the BBC. BRB meanwhile refers to the episode as The Stampede. The second Polish dub's title translates as Fortune Favors the Brave
Episode 20 gives the title as Warpaint in the West, while the preview in episode 19 calls it Adventure in the Wild West. BRB uses A Risky Decission [sic]. The BBC uses slightly different formatting for the first title, War Paint in the West.
Interestingly, in the preview for episode 21, the narrator states: "Find out in the next exciting episode of the Adventures of Willy Fog!" The Adventures of Willy Fog was an earlier title for the show, used before being renamed to Around the World with Willy Fog. This preview, along with extant Sony press releases, are the only known places where this title is used.
In another case where the episode title is not specified, both BRB and the BBC give the title as A Very Special Train. A translated version of that title is used in the second Polish dub.
The episode identifies it as Below Zero. The title is also used by the BBC, while BRB gives the title as The Return of Rigodon, despite Rigodon never leaving at any point.
The last of the no-name episodes. The BBC and both Polish dubs use Destination Liverpool, while BRB uses Destination: New York, which is incorrect, as Fog and friends leave New York in the episode.
Fire Down Below is given by the narrator in episode 23 which is also the first episode with a new narrator. BRB calls it Mutiny on the Henrietta, despite the fact that the event described was only mentioned in the previous episode, and didn't occur in the end.
The narrator names it as Last Train to London. BRB calls it The Arrest of Willy Fog, which, unlike the last few episodes, does actually occur in the episode. The second Polish dub translates to A Race Against Time
The final episode. Both it and the BBC call it What a Difference a Day Makes, while BRB calls it Final Decission [sic]. Wikipedia uses a more gramatically correct version of the title, The Final Decision.