As of the Last Jedi, we've seen the BB-series used by the First Order as well as the Resistance- what company makes them and isn't shy about selling to both sides?
Industrial Automaton is the manufacturer of BB units, among others. They have to no loyalty to either side in the various galactic conflicts, having manufactured astromechs used by both the Rebellion and the Empire, training remotes for the Jedi, and 2-1B surgical droids used by nearly every side for generations. This kind of plays into one of The Last Jedi's themes, that war profiteers don't care about what side their commodities are used for, just that they are used. So, to reiterate, Industrial Automaton is the manufacturer of BB droids.
Information courtesy of Star Wars: Galaxy's Edge—Droid Depot (it's canon)