It's actually her initials (Bridget Anna Dell), though she has tried to pass it off as meaning "Black and Dangerous", but nobody believes her. It's really a holdover from when I was little and I created several superheroes, and a couple of the silly names never went to the wayside (at the time B.A.D. really was short for "Black and Dangerous", because it was the 90s and I was a dumb kid). Multiblades is another one of the silly names, but at least it's more descriptive of her power.
In case you were curious, two characters on the team have new names from what I'd originally created for them back then. Mineral was originally Blade Jr. (and with Multiblades was on a team called the "Bladed Heroes", with such memorable characters as Blade-for-an-Arm and Bladed Eyes) and Dispawn was originally Flame Spitter (at least it's descriptive, but I have my reasons for not keeping that name, even though he still can spit flame).
I am entirely too wordy in responses to simple questions, it seems.