We've been used to using Battle.net and Blizzard almost interchangeably over the last several years, but those days are quickly coming to an end. In an announcement on the official World of Warcraft site today, Blizzard announced the beginning of the end for the Battle.net name. The core functionality of the network isn't going anywhere, so don't worry about losing your cross realm friends in World of Warcraft or your competitive Overwatch squad.
In the update, Blizzard acknowledges that there have been times where things were either confused or inefficient while trying to maintain both the Blizzard and Battle.net names. When Battle.net was first created, built-in multiplayer support was something that wasn't as common as it is today. Since it's become more of an expected feature these days, Blizzard is dropping the Battle.net name and just replacing it with Blizzard where applicable. The first steps to achieving this have already been taken with the recent Blizzard Streaming to Facebook and Blizzard Voice features not having the Battle.net name, but more instances of Battle.net will be gradually renamed to Blizzard over the next several months.
This means PC gamers will likely be running the Blizzard App instead of Battle.net App in the future to run and maintain their favorite Blizzard games, though an exact timetable for the full transition away from the Battle.net name hasn't been announced. The announcement has been met with a less than positive reception from WoW players, many of whom feel there's no reason for the change after 20 years of Battle.net.