Create a Bluetooth settings section [$50]

First, to enable Bluetooth file receiving:
 - open Terminal and run gnome-file-share-properties
 - check Receive files in Downloads over Bluetooth and Notify about received files.

Second, there are several ways to change the Bluetooth name, but this is the one I found to be permanent (i.e. not defaulting after reboot):
 - edit /etc/bluetooth/main.conf replacing "%h" with the computer name you want.

    sudo nano /etc/bluetooth/main.conf (for example change Name = %h-%d to Name = gruber)

 - find the unique hardware ID for your bluetooth hardware, list the content of /var/lib/bluetooth

     ls /var/lib/bluetooth

 - remove /var/lib/bluetooth/xx:xx:xx:xx:xx:xx/config to make your system forget the old name.

    sudo rm /var/lib/bluetooth/xx:xx:xx:xx:xx:xx/config

 - restart the bluetooth service

     sudo service bluetooth restart

thanks to: http://askubuntu.com/questions/80960/how-to-change-bluetooth-device-name/650364#650364

Maybe those two check-boxes in gnome-file-share-properties should be enabled by default, and the Bluetooth name could be automatically pulled from /etc/hostname...

Relevant bug:

 https://bugs.launchpad.net/elementaryos/+bug/1271294

Randomly works with other Elementary machines, but fails with most Windows distros. Checked with Windows 10 and continues to fail on the Elementary side.

It looks like these are settings held at org.gnome.desktop.file-sharing and the default values are:

bluetooth-accept-files bonded
bluetooth-notify true
bluetooth-obexpush-enabled false

https://www.bountysource.com/issues/33889333-create-a-bluetooth-settings-section

Hey OP, just so you're aware I'm tracking the issue separately about settings the hostname at https://bugs.launchpad.net/switchboard-plug-sharing/+bug/1234997