I recently got a 16" MacBook Pro. My wife has a 2019 15" MacBook Pro. They're both running 10.15.1 (Software Update says both Macs are "up to date").
Ever since I got the 16" MBP both MBPs are constantly trying to connect to each other via Bluetooth:
If I ignore the prompt it goes away after two seconds. If I click check "Ignore this device" and click "Cancel" the prompt comes back after two seconds. If I click "Connect" nothing happens on either MBP and the prompt keeps appearing every few seconds.
On my wife's 15" MBP System Preferences > Bluetooth list I clicked the "X" icon next to my 16" MBP's name. After doing this a different Bluetooth device name appears in her Bluetooth list after each prompt on my MBP.
The only way I've discovered to prevent this is to turn off Bluetooth on my 16" MBP.
Any ideas on how to stop these constant Bluetooth Connection Request prompts?