Is the modelname of a flight management system chosen in accordance with the aircraft it will be used on? I am looking for information about what modules (not necessarly partnumbers) are used in a flight management system of a relatively new airplane.
After having looked around for quite some time, I found this bit of information with a very nice scheme block. 

The flight management system (FMS) they are talking about is the 737 FCMS. However it is not totally clear to me (even after having looked around online), whether this is the FCMS is the one being used for Boeings 737.

Is this the case? Or is that number just coincidence?
Yes, this is the system used on the Boeing 737. As the document mentions, it is similar to the system design on the Boeing 757 and 767 models.