I will not change anything in the firmware I just want to understand if this function has a name or is it just SMART
You can NOT change the firmware, even if you want to, except you're working at the HD manufacturer at the technical department that have the knowledge specific in that area.
What ever function that you're looking for like sector error, reallocation and etc, is just the generic terms in magnetic disk storage technology.
SMART is just a reporting, see it as like your car's dashboard, it tells you your fuel level, engine temperature, speed and etc.
What are you asking is like how the gear change and drive the wheels, or what the route of the fuel pipe from the tank to the engine, your dashboard (SMART) does NOT show you that information.
Even you know how the gear changes or how the fuel pipe route to engine, it does NOT mean you can access/repair that, unless you are QUALIFIED car technician specifically for that car model, in this case the HD manufacturer's technical staff only.
And again,
NO ... you can not easily find that information on Google, that you think once you found it, you can do/fix/change the fuel routing yourself in your car, forget it.
I guess you have trouble understanding English ?