I don’t think that Rey is a Kenobi, but I also have to point out that your read on Obi-Wan seems off. He’s definitely depicted as having attachments in the Clone Wars TV series, and I think an argument can be made that he would have learned the opposite lesson from Anakin’s fall — it wasn’t Anakin’s attachments that led him to the dark side, it was his obsession over the forbidden. Plus, if there’s any moral to the story of the original trilogy, it’s that Luke love for his father is what ends up triumphing. A Jedi with no true attachments would have just killed Vader, I’m fairly certain (and not in a fit of passion — in a cold, this-is-what-Jedi-do-to-Sith way).
The Jedi order was super messed up in the years leading to their fall. They followed their code blindly, completely sure they had it figured out. And what did it lead to? They were literally doing the bidding of their sworn enemies for the last part of their existence. They carried out a war (should have been a major no-go for Jedi) that was orchestrated by a Sith lord.
It was Qui-Gon who honestly had a lot of this stuff figured out. He embraced the light side of the force first, the Jedi code second. Which is why he was never allowed onto the council. But it’s also why he was the one to discover how to become a Force ghost — something the Jedi Order viewed as a near-heretical belief.
Anyway I’m off on a rabbit trail. TL;DR: I don’t think Obi-Wan is really committed to the Jedi order in the way that you’re saying. I think he recognizes a lot of what the Jedi used to believe was off-base. But despite all that, Rey is definitely a Skywalker.