(Updated URLs)
Many bluetooth low energy profiles provide a service called Device Information
.
Assigned UUID: 0x180A
https://www.bluetooth.com/specifications/gatt/services/
Under this service there is a Serial Number String
characteristic which can hold a serial number specific to the Bluetooth low energy device.
Assigned UUID: 0x2A25
https://www.bluetooth.com/specifications/gatt/characteristics/
This is optional though and not all BLE profiles will have it, and you have to connect to the device to retrieve this information.