the b in rbx stands for base. It is just a name but it's widely accepted and good practice to use registers accordingly. e.g: use the counter register (rcx) when counting up in a loop.
Depending on the assembler, which registers you use shouldn't matter. I don't remember which one, but there is one where you can only use ebx as an offset like: mov eax,[ebx+5]. It wouldn't accept mov eax,[ecx+5]
As for the rest, you're missing an operand ( the source operand ). It should look like this: mov byte ptr[rbx],value. the 'byte' in this instruction is saying: take one byte from 'value' and move it into the address of rbx. So if value was equal to 256, it would be moving the value 0 into the address of rbx.