How are the BNR and BCD data formats identified in an ARINC-429 message?
The receiver has to be programmed.  It's important to remember that A429 is a unidirectional hard-wired bus with a single transmitter and multiple receivers.  Each connection is physically unique and the reason for all the pin-out diagrams and bus definitions in the ARINC Characteristics.  

To help with data integrity and fault detection, each transmitter includes Label 377 on the bus which contains its equipment ID.  For each type of equipment, the label assignments and coding are fixed.  

So, if you're building an LRU that's receiving GPS data, you would program the port assigned as the GPS#1 Input to verify the equipment code is 00B hex and the find the specific labels your LRU needs (it's likely to be a small subset of all data on the bus).  Since you know the source LRU and the Labels you're looking for, you know the individual label coding and can program the receiver to decode the data.  

Most avionics companies have developed custom ASICs to act as the A429 UART.  It simplifies the design and saves costs.