Since the nitrogen development board mainly targets Zephyr RTOS, I suppose there is no deal with mbed and so nitrogen is not referenced on their website (https://www.mbed.com/en/about-mbed/mbed-enabled/).
Actually, this number (board-id) seems specific to the CMSIS-DAP interface/micro-controller itself, not to the nrf52. CMSIS-DAP is the interface allowing you to flash and debug the nrf52 micro-controller via USB (pyocd, drag-and-drop…), In your case this CMSIS-DAP interface is part of the nitrogen board (LPC11U35 microcontroller), this is not always the case.
You can find some board-id info in the pyocd source code: https://github.com/mbedmicro/pyOCD/blob/master/pyOCD/board/mbed_board.py
On my side, I have 2 nrf ble-nano v2 chips and 2 daplink debug boards, one has an unknown board-id (1093), the other returns a nrf51 board-id (1095). I have no problem to flash the boards, I usually use the drag-and-drop method.
If you really want to change this board ID I think you will have to change the DAPLink firmware and then flash the LPC11U35, this can be achieved by booting in maintenance mode, usually done by pressing reset, plug usb and release reset, then your device should be detected/mounted as a ‘MAINTAINANCE’ driver. DAPLink is available here: https://github.com/ARMmbed/DAPLink/ and board id are statically defined in source/board.