I suspect the esoteric reason for naming it BLM is that BLM's luciferian creators want to tip their cap to the demon Balam, which is mentioned in their satanic ritual texts like the Lesser Key of Solomon.

In many of their rituals, they remove the vowels from the names of the demons when they are writing out curses; thus, Balam redues to B-L-M. They think that by having Balam's name (even in this shortened form) read and heard ad nauseum by millions of people through MSM, it somehow strengthens this demon and he will in turn recompense them with power, success, wealth, etc.