'WWW' is about as brand unfriendly as you can get:
1. It is not distinctive.
2. It probably confuses many surfers who don't understand domains/ subdomains, etc..
3. It is at the end of any alphabetical listing.
4. "Double U, Double U, Double U" would be awkward in a radio spot.
That said, it is a good name to use for the traffic, as actnow suggests.
I would use the traffic to push something more brandable and marketable. The way they are using the domain now is bone-headed, IMO.