The manga release of the original series kept the Japanese names of everything except the cards (in order to make the connection to the real world cards clearer) and Pegasus due to a lack of coordination in the licensing. The GX manga release always used dub names for characters that appeared in the anime.
Yugi Mutou kept his name, but its pronunciation changed so his last name sounded like "Moto".
Katsuya Jyonouchi to Joey Wheeler
Hiroto Honda to Tristan Taylor
Anzu Mazaki to Téa Gardner
Sugoroku Mutou to Solomon Moto
Mai Kujaku to Mai Valentine
Shizuka Kawai to Serenity Wheeler
Ryuji Otogi to Duke Devlin
Pegasus J. Crawford to Maximillion Pegasus, though just referred to as "Pegasus" either way.
"Bandit" Keith S. Howard became just Bandit Keith in the dub, as if it was his actual name.
Happened with some of the card names too, a few of which were in English in the original Japanese. For example, Black Magician and Black Magician Girl became Dark Magician and Dark Magician Girl (and the card's corresponding attack was changed from Black Magic to Dark Magic Attack). One of the more egregious changes was renaming Osiris no Tenkūryū (Sky Dragon of Osiris) to Slifer the Sky Dragon after one of the executive producers of the 4Kids Entertainment dub.
And odd example with the Kaiba brothers: both Seto and Mokuba kept their names, but the gang refers to Seto by his surname while referring to his brother by first name in the dub. While a Japanese audience is used to calling someone by surname as a sign of respect, for a Western audience calling someone by surname can come across as rude (which sort of worked, since the gang and Seto Kaiba don't get along whereas the gang are generally on good terms with Mokuba).
Blue-Eyes White Dragon's attack was changed from Horobi no Burst Stream (Burst Stream of Destruction) to White Lightning, creating a Dub-Induced Plot Hole when a card called Burst Stream of Destruction was used in Yu-Gi-Oh! GX.
Yūki Jūdai to Jaden Yuki (his nickname was changed from Dropout Boy to Slifer Slacker)
Tenjōin Asuka to Alexis Rhodes
Edo Phoenix to Aster Phoenix
Manjōme Jun to Chazz Princeton (his nickname was changed from Manjoume Thunder to The Chazz)
Marufuji Shō to Syrus Truesdale
Marufuji Ryō to Zane Truesdale
Amon Garam to Adrian Gecko
Tenjōin Fubuki to Atticus Rhodes
Austin O'Brien to Axel Brodie
Misawa Daichi to Bastion Misawa
Saotome Rei to Blair Flannigan
Samejima-kōchō to Chancellor Sheppard
Maeda Hayato to Chumley Huffington
Makurada Junko to Jasmine
Napoleon to Jean-Louis Bonaparte
Johan Andersen to Jesse Anderson
Daitokuji-sensei to Lyman Banner
Kanō Martin to Marcel Bonaparte
Hamaguchi Momoe to Mindy
Satō Kōji to Mr. Stein
Tome-san to Ms. Dorothy
Darkness to Nightshroud
Saiō Takuma to Sartorius
Professor Cobra to Professor Thelonious Viper
Tyranno Kenzan to Tyranno Hassleberry
Cronos de Medici to Vellian Crowler
Osiris Red to Slifer Red
Averted with the manga-exclusive characters, such as Ryuga, Seika Kohinata, and Koyo and Midori Hibiki.
Yu-Gi-Oh! 5Ds: Almost everyone and everything. But like Yugi and Kaiba's in DM, Yusei and Jack's names were unchanged. (With the exception of one 'u' in Yusei being left out, much like Yugi.)
Aki Izayoi -> Akiza Izinski
Brave -> Brodor
Carly Nagisa -> Carly Carmine
Demak -> Devack
Divine -> Sayer
Harald -> Halldor
Jaeger -> Lazar
Jose -> Jakob
Kyosuke Kiryu -> Kalin Kessler
Lucciano -> Lester
Mizoguchi -> Elsworth
Misty Lola -> Misty Tredwell
Placido -> Primo
Rua -> Leo (not to be confused with Zora's son Leo from Season 3)
Ruka -> Luna
Rudger Godwin -> Roman Goodwin
Mikage Sakari -> Mina Simington
Tetsu Ushio -> Tetsu Trudge
Minor characters:
Akutsu -> Zigzig | Bommer -> Greiger | Blitz -> Nervin | Mukuro Enjo -> Hunter Pace | Jill de Lancebeaux -> Randsborg | Jin Himuro -> Bolt Tanner | Leo -> Lyndon | Nerve -> Blitz | Saiga -> Blister | Taka -> Tank | Takasu -> Armstrong | Tenpei -> Dexter | Uryu > Lenny
and many more.
Monsters, though it's not really their fault as the TCG people at Konami changed the names officially for the Western release. Listed below are some examples, though the name changes are far too many to list.
Red Daemon's Dragon -> Red Dragon Archfiend
Savior Star Dragon -> Majestic Star Dragon
Road Runner -> Sonic Chick (Most likely done to avoid copyright infringements with Looney Tunes' Road Runner.)
Deformers -> Morphtronics
Black Feathers -> Blackwings
Earthbound God (Jibakushin) -> Earthbound Immortal
Machine Emperor (Kikoutei) -> Meklord Emperornote (The English dub intially called the Kikoutei by their translated Japanese name of "Machine Emperors" but once Konami released them in the TCG as "Meklord Emperors" the English dub started using the name "Meklord Emperors" as well.)
Polar Gods -> The Aesir
Road Warrior was called "Road Fighter" in its three English dub appearances (in epsiodes 45, 46 and 106) despite keeping its Japanese name of Road Warrior in the TCG. It is speculated that this was done to avoid copyright troubles with the 1981 film Mad Max 2, released in America as The Road Warrior.
A weird inversion of this trope occured as well. The monster cards "Tuningware" and "Fortress Warrior" note (Both monsters appear in episode 21; Tuningware/Tuning Supporter also appears in episodes 45 and 122, the latter of which has yet to premiere in English) keep their Japanese names of "Tuning Supporter" and "Massive Warrior" (respectively) in the English dub, ignoring their TCG names.
Terminology:
D-Wheel -> Duel Runner
Riding Duel -> Turbo Duel
Momentum -> Ener-D
Duel of Fortune Cup -> shortened to "Fortune Cup"
M.I.D.S. -> R.D.D. (Reactor Research Divison)
Underworld -> Netherworld
Team Satisfaction -> The Enforcers
Public Security Maintenance Bureau -> Sector Security
Dragon Birthmark -> Mark of the Dragon
Duel of Darkness -> Shadow Duel
World Riding Duel Grand Prix -> World Racing Grand Prix (Notably, as the Japanese version often omits the 'Duel', both names have the same acronym)
Riding Roid -> Duelbot
Ark Cradle -> Divine Temple (unconfirmed, but episode 106 and related episodes appear to suggest this)
In a weird variation, while Yuto, Yugo, Yuri, and Z-ARC maintain their names, the onscreen spelling has changed to match how they sound, as opposed to Ute, Hugo, Joeri and Zarc
Serena > Celina
Ruri Kurosaki > Lulu Obsidian (Justified, as Word of Saint Paul claimed that every attempt to say the name without an accent resulted in a lot of Corpsing)
Noboru Gongenzaka > Gong Strong
Shingo Sawatari > Sylvio Sawatari
Reiji Akaba > Declan Akaba (the surname is now pronounced acker-bar, rather than ack-harbour)
Syun Kurosaki > Shay Obsidian
Himika Akaba > Henrietta Akaba
Layra Akaba > Riley Akaba
Hikage and Tsukikage Fuma > Sun Shadow and Moon Shadow
Mr. Sawatari receives the forename “Furio”
Syuzo Hiragi > Skip Boyle
Futoshi, Tatsuya and Aya > Frederick, Tate and Allie