Their logos never included the Bs anyway, so I'm surprised they didn't get rid of those words earlier. They're legacy from the BSB merger after all, and that was 24 years ago!
There's a difference between a corporate name and a brbrand though. The lack of one in the other is irrelevant
One thing the BSkyB name was useful for their staff email addresses, the Sky.com ones being given out to their ISP customers. I wonder what they'll choose instead?
This incidently is an issue Yahoo had many years ago.