Having this issue as well. It's insanely frustrating, I was unaware that we have 2 different ps4s in the house. I thought someone just moved the one to another room and this issue started. Today they tell me that they actually purchased the second one from craigslist second hand. THIS one is killing my network, both wired and wireless devices have the bandwidth drained whenever this "PS4-16B8C78E6DDE" network is within range. I have 70Mbs download 5Mbs upload speeds for our network... But this thing is draining our bandwidth causing our speeds to drop as low as .9Mbs (on lan!)
I guess this is something the former owner setup, I have a very complicated network password and no one in the house has asked me for it recently, so I have no idea how this thing is even connecting let alone setting itself up as it's own network whenever they're playing on it, how do I stop it?