Should BD in this sector means Brown dwarfs or Black dwarfs? The one in the sector as BD/NS/BH. And please explain why Brown/Black dwarf should be here among neutron stars and black holes. Thank you for your help.

Source: Beech, M. (2019). Introducing the stars. Cham: Springer Nature Switzerland AG.
Looking at the diagram as a whole, the bottom line seems to be the type of object that a star in that category will evolve into.  So a large star that is variable due to mass loss will explode in a type II SN and evolve to either a Black Hole, or a Neutron star (which may become variable as a pulsar but ultimately evolves to a non variable NS.
Looking down the right. We see &quot;mass exchange variables (ie novae) and dwarf novae such as U Gem or Z And will ultimately evolve into one of three types of stellar remnant: Black dwarfs, neutron stars or black holes. Black dwarfs are the final stage of evolution of white dwarfs.
Therefore I surmise that BD means Black Dwarf.