Unfortunately that’s not entirely correct.
Operating and protesting under the BLM name promotes the organization, whether people fully support them or not.
It’s a clever trick by the organization to name themselves under such a disarming idea, the basic unarguable concept that black lives do, in fact, matter. This is not a concept to be argued with, it’s a fact.
Cloak and dagger. It’s why they so vehemently oppose the All Lives Matter, which essentially says the same exact thing except without the negative connections to the BLM organization.