Well, to be fair, that's not really what happened. HP spun off Agilent to focus on end-user general IT products. Agilent was a giant hairball of a company. PE firms stripped the chipset and component divisions out of the hairball, called them "Avago", refined the business down to chipsets and away from general components, and executed a roll-up strategy on the chipset space.
What would make sense would be for Avago to do a VW/Audi or Cingular/ATT thing and assume Broadcom's branding.
I'm not sure that the "Agilent" branding does a whole lot more for a chipset business than "Avago" does.
Also: I'm guessing if you're an Avago customer, you know it. :)
Similarly: Leidos isn't really SAIC, but rather the spun-off "national security" IT products part of SAIC.