What is the software equivalent of an engineering change order?
I'd still call it an ECO.  

If the firmware is programmed into the micro in the factory, then that firmware and its specific version should be a line item on the BOM.
Changing the firmware means changing the BOM.
Changing the BOM requires an ECO.  

Following on from that, a field update of the firmware should follow a similar process to that which would be followed if a mod to the hardware were required to a unit in the field.
So if you call that an ECO, then this is also an ECO.