Well if SK intelligence services and the BBC say it's true

She's undergoing preliminary training for the role, but has not been officially appointed successor.

She's also only 13 atm, and Kim himself isn't very old at only 42, so things could easily change before any probable transition period. Making a concrete assertation that she will succeed him at this point is premature imo.

Does no one remember the media drumming up the same 'she's been made the official successor' hype about his sister ~5 years ago(and claiming Kim had died)?
All claims about the DPRK in western media should be examined very critically as almost every bit of information outside of official statements(and even those are often presented mistranslated) is provided by South Korean intelligence and sensationalistic tabloids, both of which are highly motivated to provide false information about anything related to the DPRK