Hi,
Board model is defined in board specific DTS (e.g. "STMicroelectronics STM32MP257F-EV1 Evaluation Board")
example : https://github.com/STMicroelectronics/arm-trusted-firmware/blob/v2.10-stm32mp/fdts/stm32mp257f-ev1.dts#L18
For our boards identification coding, ST use an user OTP.
used OTP is defined in board specific DTS. If not defined (i.e. 0), nothing is displayed
https://github.com/STMicroelectronics/arm-trusted-firmware/blob/v2.10-stm32mp/fdts/stm32mp257f-ev1.dts#L45
Board identification coding and how it is display is not defined by DTS. This is custom (e.g. "MB1936 Var1.0 Rev.D-01")
If you want to tailor this differently, you should update the relevant piece of code if you want to add specific to your custom board.
More info directly into code, e.g. for TF-A :
https://github.com/STMicroelectronics/arm-trusted-firmware/blob/v2.10-stm32mp/plat/st/stm32mp1/stm32mp1_private.c#L482
I think same should be done on uBoot and Kernel if you want it.
Regards.