What determines the model name displayed in System Information compared to the model number?
I think the model name shown in System Information is determined from information encoded within the serial number. It looks like the precise details of this are private to Apple, but some information is given in this MacRumors post (which includes the image below), and it looks like some sites may have reverse engineered it.



Be aware it is possible under some circumstances to change the serial number reported to the software running on the machine. Specifically: logic boards supplied by Apple to service providers have a "blank" serial number, and service providers must "serialize" them (this is only possible once, from the service provider point of view) by running some special software and providing the desired serial number via keyboard input. (This is why I suggested checking the serial number printed on the hardware in my comment on the question.)