>>1502816From Wikipedia: "The origins of Black Rock Shooter date back to an original character illustration titled "Black Rock Shooter" by illustrator Ryohei Fuke, best known by his handle 'Huke', who posted it on his blog and the online artist community Pixiv on December 26, 2007. Ryo of Supercell was inspired by the illustration and created the song "Black Rock Shooter" based on that character using vocals from the Vocaloid singing synthesizer Hatsune Miku."
So before the OVA and series and all that stuff happened, there was pretty much only that character, which looks very much like Miku, and a Miku song.
So, while BRS and Miku clearly aren't one single character or something, they're quite closely related.