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This is the most retarded argument of semantics ever.
Hololive originally was a distribution app, later becoming the name of the female branch of the service. Hololive (as in the female branch), INoNaKa (the music label), and Holostars (as in the male branch) later merged UNDER Hololive Production as a singular brand. YET those three branches of the brand remain their own entities for all intents and purposes.
Let me explain again, Cover Corporation owns Hololive Production, which includes Hololive, INoNaKa, and Holostars.