He's supposed to be the original villain from GoRanger, just with a censored name and remade suit.
I don't think the name change was a matter of censorship, but wanting to specify that Black Cross King is technically a different character to explain why he doesn't have the same personality and to excuse how easily he'll be defeated in comparison to the original Fuhrer. If anything it was probably meant as proof against fanboyish continuity nit-picking.
(I mean, if the point of it was censorship, I doubt Black Cross King would have dialog in the movie where he bluntly declares that he was once known as the Black Cross Fuhrer.)
The resurrected Brajila in that movie gives an extremely similar speech that basically establishes why he's going to be a lot dumber and more easily beaten in this film. He's a Brajila, but he's not the original Braila. So he sticks close enough to the movie reference to do his fight in an office building, but all of the character's original psychology is just gone.
He just says that he returned from hell due to the anger of all enemies killed by the Super Sentai. Personally, in general, I didn't like the way they handled him here. He came off as a random monster of the week, rather than someone of relevance to the franchise.
Black Cross King is absolutely written in the spirit of the "Monsters of the Week" who show up in Versus movies. I don't think he's meant to be anything of significance to the franchise or anything more special than that. He's probably only a Goranger reference to set up the introduction of GorenGokai-Oh and the giant robot beatdown later in the movie.
To be honest, I liked the explanation they used for how Black Cross Fuhrer resurrected as Black Cross King because it's
really in flavor for 70's tokusatsu. Back then villains got their powers from Evil as an absolute concept and a sufficiently bad baddie resurrecting through sheer hatred of his enemies wasn't out of tone at all.
I'd compare it to how Decade used its version of Apollo Geist, to set up an intentional clash of tone between the Showa-style villain and the Heisei-style heroes. For a historical series, it's a good way of showing how things have changed, while also getting to trot out some tropes that are perfectly good but have fallen into disuse.