Hihi, many of the names suggested doesn't make any technological sense at all
In BDA-1/2 I guess its short for Bryston Digital to Analog. In other words you refer to your digital inputs with the common word digital, no matter if it's USB/S-PDIF/AES-EBU.
To be concistent with your previuos meaning of "digital" in this context, I think the most reasonable name is Bryston USB to Digital audio adapter (because you have several digital outputs), or BUD-1 in short version.
Like your other products the name also tells you what it does. Although I like Bryston USB Interface for its look, a USB interface could be more or less anything from audio to file storage and serial adapters.