At the core of the group stands Ken Downie who was in the early years joined by Handley and Turner who broke away after release of the album Spanners on Warp.
There are probably no recordings that could be credited to the moniker "Black Dog Productions" except for compilation style releases. Instead Downie, Handley and Turner used various pseudonyms for their projects, probably depending on who worked on them. The distinctions between the various pseudonyms shouldn't be as clear cut as the following list suggest:
Ken Downie alone: Xeper, Discordian Popes, I.A.O.
Ed Handley alone: Close Up Over, Balil
Andy Turner alone: Atypic, Tura, Plaid (Andy alone for Bytes)
Turner + Handley: Plaid (on release other than Bytes)
Downie, Turner & Handley: The Black Dog
This doesn't prevent the Black Dog Productions from being given as artist for single tracks on many a compilation.