assuming the example you gave (i.e. no other software/tech involved), all the "BT dongles" should show up on your phone by name (as a discoverable device). If all of your dongles are the same I would imagine it would be very difficult to identify which TV a particular dongle is plugged into. You can give the BT device (the dongle) a new name on your phone(an alias). if you were to do this for each one, you would then be able to differentiate between them.
The phone would usually be used to govern permission for the connection but, seeing as you would be initiating the connection from the phone permission is essentially granted then anyway.
Bluetooth Pairing: Network Connection >> Electronics Notes
Renaming on iPhone:
Change the name of a Bluetooth accessory - Apple Support
and on Andoid:
Change Android Device Name - WiFi / Bluetooth / Hotspot Name

