The novel Kenobi, part of the Star Wars Legends series, tells the story of Obi-Wan's first days on Tatooine after the fall of the Republic. In the story, we learn that Obi-Wan took on the name Ben because it's a nickname given to him by an old flame, the Duchess Satine Kryze.
As "Ben" was Satine's nickname for Obi-Wan, it's probably why he decided to go by it during his time on Tatooine. The name "Ben" likely brought back fond memories of Obi-Wan's time with Satine, who was assassinated during Season 5 of The Clone Wars.
In the old Expanded Universe, a.k.a. Legends, it was an alias he was particularly fond of; according to John Jackson Miller's novel Kenobi, he'd been given the nickname by the Duchess Satine of Mandalore, a woman Obi-Wan had fallen in love with back when he was just a Padawan.
He's hiding under the mononym of “Ben” and anyone who knows him otherwise is protecting his privacy and thus his life. To Tatooine and the wider galaxy he's just Old Ben the hermit, full stop. AFAIK the only person to ever refer to him as “Ben Kenobi” is Luke, who no doubt learned the name from his Owen.
Ben was a name that Obi-Wan used a couple of times throughout his life. Not only was it his nickname that he and Duchess Satine used when he was assigned to her as a bodyguard when he was a padawan, when they first met during the Mandalorian Civil War, but Kenobi used the name 'Ben' as an alias during the Clone Wars.
In canon no Obi-Wan doesn't have kids. However, there is this theory where he and Satine had a child together but she hide it from him, knowing how it could ruin his jedi career. This child would be Satine's “nephew” Korkie Kryze…
During Mandalore's Civil War and his apprenticeship under Qui-Gon Jinn, Obi-Wan fell in love with the young Duchess Satine Kryze. The two lived on the run for over a year. Satine reciprocated his feelings as he saved her life from insurgents and bounty hunters.
In the original trilogy he is introduced as Ben Kenobi, an alias he uses while in hiding from the Empire. He is a mentor to Luke Skywalker, to whom he introduces the ways of the Jedi. After sacrificing himself in a duel against Darth Vader, Obi-Wan guides Luke through the Force in his fight against the Galactic Empire.
While you'd think Owen would welcome the extra security and free hardware, he believes that Obi-Wan's endgame is to train Luke as a Jedi, which he is vehemently against.
Despite learning that Anakin was still alive, Obi-Wan maintained his belief that Luke was the Chosen One. Obi-Wan believed that Luke would succeed where Anakin failed, and he had faith in Luke's ability to bring balance to the Force.
Obi-wan responds to starwars.wikia.com/wiki/Luke_Skywalker saying R2 belongs to him with, “I don't seem to remember ever owning a droid,” which is technically true, because Obi-Wan never did “own” R2 or C-3PO. Obi-Wan then makes a comment that suggests he's more than aware of R2's impressive capabilities.
🎬 [ANH] Why did Obi-Wan age so fast on Tatooine? Well, because it's TATOOINE, it is a desert planet with 2 suns so people age faster there. Which is why Obi-Wan looks like he's in his 60s in ANH when he's only 57. It would also explain why Luke looks like he's 25 in ANH when he's only 19 and Leia actually looks 19.
Having revealed that he used to be a Jedi Padawan under Luke Skywalker, Ben Solo changed his name to Kylo Ren in order to escape his lineage after turning to the dark side. However, he kept a tie to his heritage when creating his new moniker.
The leader of Mandalore during the Clone Wars, Duchess Satine of Kalevala was a controversial figure. She longed to move Mandalore beyond its violent past and instituted a government that valued pacifism.
The movie novelization, however, did include a line in which Kenobi referred to "[his] brother Owen." Similarly, Owen Lars was explicitly described as the "brother of Obi-Wan Kenobi" in the Premiere Limited set of the Star Wars Customizable Card Game released by Decipher, Inc.
The mystery of Rey's parents was kept secret for years, and Star Wars actor Daisy Ridley revealed the original idea was to have Obi-Wan as her father. For several years, Rey's heritage was the biggest question within Star Wars fandom.
This fell in line with various fan theories and non-canon novelizations that suggested Obi-Wan and Padmé had an affair sometime during the Clone Wars. In the Star Wars prequel movies, Obi-Wan often has a duty to protect Padmé, but there was never any sense of romantic feelings.
Raised as a farmer on the fictional planet Tatooine, Luke joins the Rebel Alliance and becomes a pivotal figure in the struggle against the Galactic Empire. He trains as a Jedi under Obi-Wan Kenobi and Yoda, and eventually confronts his father, the Sith Lord Darth Vader.
Ben Solo is the son of Leia Organa and Han Solo, born in 5 ABY on the day the Galactic Civil War officially came to an end. He was named after Obi-Wan “Ben” Kenobi, the Jedi Master who aided in Leia's rescue from the Death Star only five years earlier.
During his Padawan training, Obi-Wan and Qui-Gon Jinn were assigned to be bodyguards to Duchess Satine Kryze of Mandalore. They spent nearly a year together, often unsure of what fate the next day would bring. Eventually, the two fell in love, and during their private moments, Satine affectionately called him “Ben”.
