Oooh, where to start?
My list of podcasts are:
Drinking From the Toilet by Hannah Branigan
Cog Dog Radio by Sarah Stremming
Animal Training Academy (not just dogs)
Bad Dog Agility (not actually listened to any of these yet, but I hear it's good)
Dog Talk with Dr Jen (I find it a bit too basic, TBH, but they only come out every now and again, so I listen just in case)
Dog Talk with Nick Benger (only just started listening)
FDSP, which you already listen to
Hidden Brain (psychology, not just animals)
Kay Laurence - Learning About Dogs (new podcast, I've not listened yet, but have heard good things. And it's Kay Laurence!)
Pure Dog Talk (not listened yet)
The Barking Mad Show (not listened yet)
The Modern Dog Trainer (listened to a couple a while back, not got into it really)
Why We Do What We Do (human psychology, but much also applicable to animals)