I think it's already there, in Organization>Settings you have the field MSP Identification ID, not sure when they added it, never used to be there.
The API call https://developer.cisco.com/meraki/api-v1/#!get-organizations gets you that value.
I don't see it in documentation.meraki.com, but from API info it looks like it's just an optional freeform text field that you can do what you like with.
I'd say it's more like a field you could use to put something like a customer contract number in. Not something identifying an MSP itself.