Warning! Spoilers ahead for Obi-Wan Kenobi episodes 1 & 2
While Obi-Wan Kenobi's new Inquisitor Reva is obsessed with hunting down the titular Jedi master, it may be because of a secret history with Anakin Skywalker during Order 66. Considering several factors such as the Third Sister's knowledge about Darth Vader's true identity as well as teases to her origins from the Grand Inquisitor, Reva might be more connected to the Sith Lord who was once Anakin. As such, hunting Obi-Wan might not be her primary focus and is rather a means to a greater end.
As seen in Star Wars: Episode III- The Revenge of the Sith, Emperor Palpatine ordered his new apprentice Darth Vader to go to the Jedi Temple and exterminate all of the Jedi within. This included many of the younglings who were training to be future members of the Jedi Order. However, the new Obi-Wan Kenobi is potentially teasing that one may have been spared.
In Obi-Wan Kenobi episodes 1-2, Reva's Third Sister has taken center stage as the primary antagonist, being the most ambitious and aggressive in comparison to Fifth Brother and even the Grand Inquisitor himself. While her fellow Jedi hunters see her as inferior as one who "came from the gutter", Reva believes that capturing Obi-Wan for Darth Vader will grant her "what she's owed". As such, it certainly seems as though a secret history between Reva and Darth Vader himself might come to light with the theory that Reva was a youngling Anakin might have spared during Order 66.
How Third Sister Knows Darth Vader Is Anakin
In Obi-Wan Kenobi episode 2, the Third Sister is seen taunting Kenobi after luring him out of hiding, confronting him on the planet Daiyu after using Princess Leia Organa as bait. Revealing to Obi-Wan that Anakin Skywalker is alive, it's confirmed that Reva knows Darth Vader's true identity, the Jedi he once was before his corruption to the dark side in Revenge of the Sith. This is rather surprising given the intentional mystery surrounding Darth Vader's origins among those who serve in the Empire. Not only did the secret of Darth Vader's true identity amuse the Emperor, but it was also effective at making Vader's reputation far more intimidating as his primary enforcer. As such, one has to wonder how Reva knows this closely guarded secret.
While every Inquisitor may know Darth Vader's secret as a matter of protocol, it would certainly be strange even amongst the elite group of Jedi hunters who served the Sith. In Darth Vader's mind, Anakin Skywalker is dead, a separate being whom he killed in his attempt to bury his past life. It would be far more intriguing if Reva's knowledge about Anakin was a piece of information only she carries. Not only would it further motivate her ambitions to track down Kenobi as a means to gain favor with Darth Vader, but only she would know what capturing Kenobi would truly mean for the Dark Lord of the Sith.
Obi-Wan Theory: Vader Spared Reva During Order 66
If Reva is the only Inquisitor who knows Anakin and Darth Vader are one and the same, the question has to be asked as to how and when she would have made this discovery. It's possible that she was one of the younglings featured in the Order 66 flashback at the beginning of Obi-Wan Kenobi's first episode. With their master dead, the group of children were seen attempting to flee the Temple. However, an encounter with the newly christened Darth Vader might have occurred. Perhaps he spared Reva who was then inducted into the Imperial Inquisitorius. After all, many of the Empire's Jedi hunters were either kidnapped Force-sensitives or were once Jedi themselves (including the Grand Inquisitor).
While Anakin notoriously killed younglings in Revenge of the Sith, perhaps his first steps in embracing the dark side saw him extending mercy where he couldn't bring himself to kill them all, choosing to spare Reva instead. His path as Darth Vader might not have been fully cemented until after his duel with Obi-Wan and losing his wife Padmé. At any rate, Reva's obsessive hunt for Obi-Wan could very well be a by-product of her secret history with Anakin Skywalker, rather than having some sort of personal vendetta against Kenobi himself. Star Wars fans will just have to wait and see with future episodes of Obi-Wan Kenobi.
Obi-Wan Kenobi releases new episodes on Wednesdays on Disney+.