really this is a good question and i dont even really know if the one in BBS is real, maybe its the one in KH but that seems to be more of the heart of all worlds. even though when ansem the wise talked about his testing with heartless, he said doors appeared, not heart shaped moons.
I actually dont know, maybe all three of them are kingdom hearts just taken different shape/color. If not, Xemnas/Vexen could probably make some sort of heart collector to recreate it.
Another question is that since KH is a gathering of many hearts or heartless, how could there be a KH in BBS, there were no heartless and following Kairis grandmothers story, all hearts were of pure light so there could be no hearts consumed by darkness to form KH. Unless the KH in BBS is of hearts of light gathered. KH1's KH was the heart of all worlds, and KH2's Kh was a gathering of dark hearts. IDK just writing things as i go here.
Well, her story might have been a very old one that existed waaaaaay before BBS. Well, when a person dies their heart might go to KH as well.
but kh is made up of darkness that holds some light when released. i guess it could also be possible that the keyblade wielders in the war did not know there was darkness and kh is what actually created it
KH is both light and darkness since we know it is formed by hearts and hearts don't lean to either side. I don't think KH created darkness...I'm sure it always existed in some form or it was created through people and their shift in intentions.