Battle.net is being dropped in favor of a new service name. In probably the most corporate of responses Blizzard is probably going to create a service that's more associated with the company.
"We’re going to be transitioning away from using the Battle.net name for our gaming service and the functionality connected to it. Battle.net technology will continue to serve as the central nervous system for Blizzard games—nothing is changing in that regard. We'll just be referring to our various products and services using the Blizzard name instead. You've already seen this recently with things like "Blizzard Streaming" and "Blizzard Voice," and more changes are on the way.
When we created Battle.net, the idea of including a tailored online-gaming service together with your game was more of a novel concept, so we put a lot of focus on explaining what the service was and how it worked, including giving it a distinct name. Over time, though, we’ve seen that there’s been occasional confusion and inefficiencies related to having two separate identities under which everything falls—Blizzard and Battle.net. Given that built-in multiplayer support is a well-understood concept and more of a normal expectation these days, there isn’t as much of a need to maintain a separate identity for what is essentially our networking technology.
We just wanted to make sure everyone was aware as we moved forward with this change over the next several months; we’ll provide any relevant updates as the transition progresses."
I think that people who are new to Blizzard games are getting confused between Blizzard and Battle.net services since there is no brand name association. Kind of like Origins with EA even though that never seemed to be a problem for them.
My guess is with a flood of new people getting involved with Overwatch some of which have never picked up a Blizzard game there was some confusion. Also Blizzard probably wants to maintain consistency across its various platforms. Either way its gonna be the same Battle.net with a different name.